\u81ea\u7136\u6570 \\(n\\) \u306b\u5bfe\u3057, \\(3\\) \u500b\u306e\u6570\u5b57 \\(1, 2, 3\\) \u304b\u3089\u91cd\u8907\u3092\u8a31\u3057\u3066 \\(n\\) \u500b\u4e26\u3079\u305f\u3082\u306e \\(( x _ 1 , x _ 2 , \\cdots , x _ n)\\) \u306e\u5168\u4f53\u306e\u96c6\u5408\u3092 \\(S _ n\\) \u3068\u304a\u304f.\r\n\\(S _ n\\) \u306e\u8981\u7d20 \\(( x _ 1 , x _ 2 , \\cdots , x _ n)\\) \u306b\u5bfe\u3057, \u6b21\u306e \\(2\\) \u3064\u306e\u6761\u4ef6\u3092\u8003\u3048\u308b.<\/p>\r\n
\u6761\u4ef6 \\( \\text{C} {} _ {12}\\) : \\(1 \\leqq i \\lt j \\leqq n\\) \u3067\u3042\u308b\u6574\u6570 \\(i , j\\) \u306e\u7d44\u3067, \\(x _ i = 1\\) , \\(x _ j = 2\\) \u3092\u6e80\u305f\u3059\u3082\u306e\u304c\u5c11\u306a\u304f\u3068\u3082 \\(1\\) \u3064\u5b58\u5728\u3059\u308b.<\/p><\/li>\r\n
\u6761\u4ef6 \\( \\text{C} {} _ {123}\\) : \\(1 \\leqq i \\lt j \\lt k \\leqq n\\) \u3067\u3042\u308b\u6574\u6570 \\(i , j , k\\) \u306e\u7d44\u3067, \\(x _ i = 1\\) , \\(x _ j = 2\\) , \\(x _ k = 3\\) \u3092\u6e80\u305f\u3059\u3082\u306e\u304c\u5c11\u306a\u304f\u3068\u3082 \\(1\\) \u3064\u5b58\u5728\u3059\u308b.<\/p><\/li>\r\n<\/ol>\r\n
\u4f8b\u3048\u3070, \\(S _ 4\\) \u306e\u8981\u7d20 \\(( 3, 1, 2, 2 )\\) \u306f\u6761\u4ef6 \\( \\text{C} {} _ {12}\\) \u3092\u6e80\u305f\u3059\u304c, \u6761\u4ef6 \\( \\text{C} {} _ {123}\\) \u306f\u6e80\u305f\u3055\u306a\u3044.
\r\n\\(S _ n\\) \u306e\u8981\u7d20 \\(( x _ 1 , x _ 2 , \\cdots , x _ n)\\) \u306e\u3046\u3061, \u6761\u4ef6 \\( \\text{C} {} _ {12}\\) \u3092\u6e80\u305f\u3055\u306a\u3044\u3082\u306e\u306e\u500b\u6570\u3092 \\(f(n)\\) , \u6761\u4ef6 \\( \\text{C} {} _ {123}\\) \u3092\u6e80\u305f\u3055\u306a\u3044\u3082\u306e\u306e\u500b\u6570\u3092 \\(g(n)\\) \u3068\u304a\u304f. \u3053\u306e\u3068\u304d\u4ee5\u4e0b\u306e\u5404\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n
(1)<\/strong>\u3000\\(f(4)\\) \u3068 \\(g(4)\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n (2)<\/strong>\u3000\\(f(n)\\) \u3092 \\(n\\) \u3092\u7528\u3044\u3066\u8868\u305b.<\/p><\/li>\r\n (3)<\/strong>\u3000\\(g(n+1)\\) \u3092 \\(g(n)\\) \u3068 \\(f(n)\\) \u3092\u7528\u3044\u3066\u8868\u305b.<\/p><\/li>\r\n (4)<\/strong>\u3000\\(g(n)\\) \u3092 \\(n\\) \u3092\u7528\u3044\u3066\u8868\u305b.<\/p><\/li>\r\n<\/ol>\r\n (1)<\/strong><\/p>\r\n \\(S _ 4\\) \u306e\u8981\u7d20\u306e\u6570\u306f\u5168\u90e8\u3067\r\n\\[\r\n3^4 = 81 \\ \\text{\u901a\u308a} \\ .\r\n\\]\r\n \\(f(4)\\) \u306b\u3064\u3044\u3066 1*<\/strong>\u3000\\(S _ n = \\{ 1, 1, 1, 2 \\}\\) \u306e\u3068\u304d 2*<\/strong>\u3000\\(S _ n = \\{ 1, 1, 2, 2 \\}\\) \u306e\u3068\u304d 3*<\/strong>\u3000\\(S _ n = \\{ 1, 2, 2, 2 \\}\\) \u306e\u3068\u304d 4*<\/strong>\u3000\\(S _ n = \\{ 1, 1, 2, 3 \\}\\) \u306e\u3068\u304d 5*<\/strong>\u3000\\(S _ n = \\{ 1, 1, 2, 3 \\}\\) \u306e\u3068\u304d 6*<\/strong>\u3000\\(S _ n = \\{ 1, 2, 3, 3 \\}\\) \u306e\u3068\u304d \u4e0a\u8a18\u4ee5\u5916\u306e\u6570\u5b57\u306e\u7d44\u5408\u305b\u306f\u6761\u4ef6\u3092\u6e80\u305f\u3055\u306a\u3044. \\(g(4)\\) \u306b\u3064\u3044\u3066 1*<\/strong>\u3000\\(S _ n = \\{ 1, 1, 2, 3 \\}\\) \u306e\u3068\u304d 2*<\/strong>\u3000\\(S _ n = \\{ 1, 2, 2, 3 \\}\\) \u306e\u3068\u304d 3*<\/strong>\u3000\\(S _ n = \\{ 1, 2, 3, 3 \\}\\) \u306e\u3068\u304d \u4e0a\u8a18\u4ee5\u5916\u306e\u6570\u5b57\u306e\u7d44\u5408\u305b\u306f\u6761\u4ef6\u3092\u6e80\u305f\u3055\u306a\u3044. (2)<\/strong><\/p>\r\n \u3068\u304a\u304f. \\(x _ {n+1} = 2\\) \u3067\u3042\u308b\u8981\u7d20\u306f, \\(S _ n\\) \u304c\u6761\u4ef6 \\( \\text{C} {} _ 1\\) \u3092\u6e80\u305f\u3057\u3066\u3044\u306a\u3044.<\/p><\/li>\r\n \\(x _ {n+1} = 1 , 3\\) \u3067\u3042\u308b\u8981\u7d20\u306f, \\(S _ n\\) \u304c\u6761\u4ef6 \\( \\text{C} {} _ {12}\\) \u3092\u6e80\u305f\u3057\u3066\u3044\u306a\u3044.<\/p><\/li>\r\n<\/ul>\r\n \u3086\u3048\u306b, [1] \u3082\u7528\u3044\u308c\u3070\r\n\\[\\begin{align}\r\nf(n+1) & = d(n) +2 f(n) \\\\\r\n\\text{\u2234} \\quad \\dfrac{f(n+1)}{2^{n+1}} & = \\dfrac{1}{2} +\\dfrac{f(n)}{2^n} \\ .\r\n\\end{align}\\]\r\n\u6570\u5217 \\(\\left\\{ \\dfrac{f(n)}{2^n} \\right\\}\\) \u306f, \u521d\u9805 \\(\\dfrac{f(1)}{2} = \\dfrac{3}{2}\\) , \u516c\u5dee \\(\\dfrac{1}{2}\\) \u306e\u7b49\u5dee\u6570\u5217\u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\dfrac{f(n)}{2^n} & = \\dfrac{3}{2} +\\dfrac{n-1}{2} = \\dfrac{n+2}{2} \\\\\r\n\\text{\u2234} \\quad f(n) & = \\underline{(n+2) 2^{n-1}} \\ .\r\n\\end{align}\\]\r\n (3)<\/strong><\/p>\r\n (2)<\/strong> \u3068\u540c\u69d8\u306b\u8003\u3048\u3066, \u96c6\u5408 \\(S _ {n+1}\\) \u306e\u4e2d\u3067, \u6761\u4ef6 \\( \\text{C} {} _ {123}\\) \u3092\u6e80\u305f\u3055\u306a\u3044\u3082\u306e\u306e\u3046\u3061<\/p>\r\n \\(x _ {n+1} = 3\\) \u3067\u3042\u308b\u8981\u7d20\u306f, \\(S _ n\\) \u304c\u6761\u4ef6 \\( \\text{C} {} _ {12}\\) \u3092\u6e80\u305f\u3057\u3066\u3044\u306a\u3044.<\/p><\/li>\r\n \\(x _ {n+1} = 1 , 2\\) \u3067\u3042\u308b\u8981\u7d20\u306f, \\(S _ n\\) \u304c\u6761\u4ef6 \\( \\text{C} {} _ {123}\\) \u3092\u6e80\u305f\u3057\u3066\u3044\u306a\u3044.<\/p><\/li>\r\n<\/ul>\r\n \u3088\u3063\u3066\r\n\\[\r\ng(n+1) = \\underline{f(n) +2 g(n)} \\ .\r\n\\]\r\n (4)<\/strong><\/p>\r\n (2)<\/strong> \u306e\u7d50\u679c\u3082\u7528\u3044\u3066, (3)<\/strong> \u306e\u7d50\u679c\u3092\u5909\u5f62\u3059\u308b\u3068\r\n\\[\r\n\\dfrac{g(n+1)}{2^{n+1}} = \\dfrac{g(n)}{2^n} +\\dfrac{n+2}{4} \\ .\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, \u6570\u5217 \\(\\left\\{ \\dfrac{g(n)}{2^n} \\right\\}\\) \u306e\u968e\u5dee\u6570\u5217\u3092\u8003\u3048\u308c\u3070\r\n\\[\\begin{align}\r\n\\dfrac{g(n)}{2^n} & = \\dfrac{g(1)}{2} +\\textstyle\\sum\\limits _ {k=1}^{n-1} \\dfrac{k+2}{4} \\\\\r\n& = \\dfrac{3}{2} +\\dfrac{1}{4} \\left\\{ \\dfrac{n (n-1)}{2} +2 (n-1) \\right\\} \\\\\r\n& = \\dfrac{n^2 +3n +8}{8} \\\\\r\n\\text{\u2234} \\quad g(n) & = \\underline{\\left( n^2 +3n +8 \\right) 2^{n-3}} \\ .\r\n\\end{align}\\]\r\n (2)<\/strong><\/p>\r\n \u6761\u4ef6 \\( \\text{C} {} _ {12}\\) \u3092\u6e80\u305f\u3059 \\(S _ n\\) \u306e\u8981\u7d20\u306e\u500b\u6570 \\(\\overline{f(n)}\\) \u3092\u8003\u3048\u308b. \\(a _ 1 , \\cdots , a _ {k-1}\\) \u306f, \\(2 , 3\\) \u306e\u307f\u3067, \\(2^{k-1}\\) \u901a\u308a. \uff08 \\(k = 1\\) \u306e\u3068\u304d\u3082\u6e80\u305f\u3059. \uff09<\/p><\/li>\r\n \\(a _ {k+1} , \\cdots , a _ n\\) \u306f, \u5c11\u306a\u304f\u3068\u3082 \\(1\\) \u3064\u306e \\(2\\) \u3092\u542b\u3080\u306e\u3067, \\(3^{n-k} -2^{n-k}\\) \u901a\u308a.<\/p><\/li>\r\n<\/ul>\r\n \u3057\u305f\u304c\u3063\u3066\r\n\\[\\begin{align}\r\n\\overline{f(n)} & = \\textstyle\\sum\\limits _ {k=1}^{n-1} 2^{k-1} \\left( 3^{n-k} -2^{n-k} \\right) \\\\\r\n& = \\textstyle\\sum\\limits _ {k=1}^{n-1} \\left\\{ 3^{n-1} \\left( \\dfrac{2}{3} \\right)^{k-1} -2^{n-1} \\right\\} \\\\\r\n& = 3^{n-1} \\cdot \\dfrac{1 -\\left( \\frac{2}{3} \\right)^{n-1}}{1 -\\frac{2}{3}} -(n-1) 2^{n-1} \\\\\r\n& = 3^n -3 \\cdot 2^{n-1} -(n-1) 2^{n-1} \\\\\r\n& = 3^n -(n+2) 2^{n-1} \\ .\r\n\\end{align}\\]\r\n\u3088\u3063\u3066\r\n\\[\r\nf(n) = 3^n -\\overline{f(n)} = \\underline{(n+2) 2^{n-1}} \\ .\r\n\\]\r\n (4)<\/strong><\/p>\r\n (2)<\/strong> \u3068\u540c\u69d8\u306b, \u6761\u4ef6 \\( \\text{C} {} _ {123}\\) \u3092\u6e80\u305f\u3059 \\(S _ n\\) \u306e\u8981\u7d20\u306e\u500b\u6570 \\(\\overline{g(n)}\\) \u3092\u8003\u3048\u308b. \\(a _ 1 , \\cdots , a _ {k-1}\\) \u306f, \\(2 , 3\\) \u306e\u307f\u3067, \\(2^{k-1}\\) \u901a\u308a. \uff08 \\(k = 1\\) \u306e\u3068\u304d\u3082\u6e80\u305f\u3059. \uff09<\/p><\/li>\r\n \\(a _ {k+1} , \\cdots , a _ {\\ell -1}\\) \u306f, \\(1 , 3\\) \u306e\u307f\u3067, \\(2^{\\ell -k-1}\\) \u901a\u308a. \uff08 \\(\\ell -k = 1\\) \u306e\u3068\u304d\u3082\u6e80\u305f\u3059. \uff09<\/p><\/li>\r\n \\(a _ {\\ell +1} , \\cdots , a _ n\\) \u306f, \u5c11\u306a\u304f\u3068\u3082 \\(1\\) \u3064\u306e \\(3\\) \u3092\u542b\u3080\u306e\u3067, \\(3^{n -\\ell} -2^{n -\\ell}\\) \u901a\u308a.<\/p><\/li>\r\n<\/ul>\r\n \u3057\u305f\u304c\u3063\u3066\r\n\\[\\begin{align}\r\n\\overline{g(n)} & = \\textstyle\\sum\\limits _ {\\ell = 2}^{n-1} \\textstyle\\sum\\limits _ {k=1}^{\\ell -1} 2^{k-1} \\cdot 2^{\\ell -k-1} \\left( 3^{n -\\ell} -2^{n -\\ell} \\right) \\\\\r\n& = \\textstyle\\sum\\limits _ {\\ell = 2}^{n-1} ( \\ell -1 ) 2^{\\ell -2} \\left( 3^{n -\\ell} -2^{n -\\ell} \\right) \\\\\r\n& = \\textstyle\\sum\\limits _ {\\ell = 1}^{n-2} \\ell \\cdot 2^{\\ell -1} \\left( 3^{n -\\ell -1} -2^{n -\\ell -1} \\right) \\\\\r\n& = \\textstyle\\sum\\limits _ {\\ell = 1}^{n-2} \\left\\{ 3^{n-2} \\ell \\left( \\dfrac{2}{3} \\right)^{\\ell -1} -2^{n-2} \\ell \\right\\} \\\\\r\n& = 3^{n-2} \\underline{\\textstyle\\sum\\limits _ {\\ell = 1}^{n-2} \\ell \\left( \\dfrac{2}{3} \\right)^{\\ell -1}} _ {[2]} -2^{n-2} \\cdot \\dfrac{(n-1)(n-2)}{2} \\ .\r\n\\end{align}\\]\r\n\u3053\u3053\u3067, \u4e0b\u7dda\u90e8 [2] \u306b\u3064\u3044\u3066\r\n\\[\\begin{align}\r\n[2] & = 1 \\cdot 1 +2 \\cdot \\dfrac{2}{3} + \\cdots +(n-2) \\left( \\dfrac{2}{3} \\right)^{n-3} \\quad ... [3] , \\\\\r\n[2] \\times \\dfrac{2}{3} & = 1 \\cdot \\dfrac{2}{3} + \\cdots +(n-3) \\left( \\dfrac{2}{3} \\right)^{n-3} +(n-2) \\left( \\dfrac{2}{3} \\right)^{n-2} \\quad ... [4] \\ .\r\n\\end{align}\\]\r\n\\(( [3] -[4] ) \\times 3\\) \u3088\u308a\r\n\\[\\begin{align}\r\n[2] & = 3 \\left\\{ 1 +\\dfrac{2}{3} + \\cdots +\\left( \\dfrac{2}{3} \\right)^{n-3} -(n-2)\\left( \\dfrac{2}{3} \\right)^{n-2} \\right\\} \\\\\r\n& = 3 \\cdot \\dfrac{1 -\\left( \\frac{2}{3} \\right)^{n-2}}{1 -\\frac{2}{3}} -3 (n-2) \\left( \\dfrac{2}{3} \\right)^{n-2} \\\\\r\n& = 3^2 -3 (n+1) \\left( \\dfrac{2}{3} \\right)^{n-2} \\ .\r\n\\end{align}\\]\r\n\u3086\u3048\u306b\r\n\\[\\begin{align}\r\n\\overline{g(n)} & = 3^{n} -3 (n+1) 2^{n-2} -(n-1)(n-2) 2^{n-3} \\\\\r\n& = 3^n -\\left( n^2 +3n +8 \\right) 2^{n-3} \\ .\r\n\\end{align}\\]\r\n\u3088\u3063\u3066\r\n\\[\r\ng(n) = 3^n -\\overline{g(n)} = \\underline{\\left( n^2 +3n +8 \\right) 2^{n-3}} \\ .\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u81ea\u7136\u6570 \\(n\\) \u306b\u5bfe\u3057, \\(3\\) \u500b\u306e\u6570\u5b57 \\(1, 2, 3\\) \u304b\u3089\u91cd\u8907\u3092\u8a31\u3057\u3066 \\(n\\) \u500b\u4e26\u3079\u305f\u3082\u306e \\(( x _ 1 , x _ 2 , \\cdots , x _ n)\\) \u306e\u5168\u4f53\u306e\u96c6\u5408\u3092 \\(S … \u7d9a\u304d\u3092\u8aad\u3080
\r\n\r\n\u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n
\r\n
\r\n\u6761\u4ef6 \\( \\text{C} {} _ {12}\\) \u3092\u6e80\u305f\u3059\u8981\u7d20\u306e\u6570\u3092, \\(S _ 4\\) \u306b\u542b\u307e\u308c\u308b\u6570\u5b57\u306e\u7d44\u5408\u305b\u3067\u5834\u5408\u5206\u3051\u3057\u3066, \u6570\u3048\u308b.<\/p>\r\n\r\n
\r\n\\({} _ 4 \\text{C} {} _ 1 = 4\\) \u901a\u308a\u306e\u8981\u7d20\u304c\u3042\u308a, \\(( 2, 1, 1, 1 )\\) \u4ee5\u5916\u306f\u6761\u4ef6\u3092\u6e80\u305f\u3059\u306e\u3067\r\n\\[\r\n4 -1 = 3 \\ \\text{\u901a\u308a} \\ .\r\n\\]<\/li>\r\n
\r\n\\({} _ 4 \\text{C} {} _ 2 = 6\\) \u901a\u308a\u306e\u8981\u7d20\u304c\u3042\u308a, \\(( 2, 2, 1, 1 )\\) \u4ee5\u5916\u306f\u6761\u4ef6\u3092\u6e80\u305f\u3059\u306e\u3067\r\n\\[\r\n6 -1 = 5 \\ \\text{\u901a\u308a} \\ .\r\n\\]<\/li>\r\n
\r\n\\({} _ 4 \\text{C} {} _ 1 = 4\\) \u901a\u308a\u306e\u8981\u7d20\u304c\u3042\u308a, \\(( 2, 2, 2, 1 )\\) \u4ee5\u5916\u306f\u6761\u4ef6\u3092\u6e80\u305f\u3059\u306e\u3067\r\n\\[\r\n4 -1 = 3 \\ \\text{\u901a\u308a} \\ .\r\n\\]<\/li>\r\n
\r\n\u300c \\(1, 1, 2\\) \u300d\u307e\u305f\u306f\u300c \\(1, 2, 1\\) \u300d\u3068\u3044\u3046\u4e26\u3073\u306b, \\(3\\) \u3092\u8ffd\u52a0\u3059\u308b\u65b9\u6cd5\u304c \\({} _ 4 \\text{C} {} _ 1 = 4\\) \u901a\u308a\u3042\u308b\u306e\u3067\r\n\\[\r\n2 \\cdot 4= 8 \\ \\text{\u901a\u308a} \\ .\r\n\\]<\/li>\r\n
\r\n4*<\/strong>\u3068\u540c\u69d8\u306b\u8003\u3048\u3066\r\n\\[\r\n2 \\cdot 4= 8 \\ \\text{\u901a\u308a} \\ .\r\n\\]<\/li>\r\n
\r\n\u300c \\(1, 2\\) \u300d\u3068\u3044\u3046\u4e26\u3073\u306b, \\(2\\) \u3064\u306e \\(3\\) \u3092\u8ffd\u52a0\u3059\u308b\u65b9\u6cd5\u3092\u8003\u3048\u308c\u3070\u3088\u3044\u306e\u3067\r\n\\[\r\n{} _ 3 \\text{C} {} _ 1 + {} _ 3 \\text{C} {} _ 2 = 6 \\ \\text{\u901a\u308a} \\ .\r\n\\]<\/li>\r\n<\/ol>\r\n
\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u5024\u306f\r\n\\[\r\nf(4) = 81 -( 3+5+3+8+8+6 ) = \\underline{48} \\ .\r\n\\]<\/li>\r\n
\r\n\\(f(4)\\) \u3068\u540c\u69d8\u306b\u8003\u3048\u308b.<\/p>\r\n\r\n
\r\n\u300c \\(1, 2, 3\\) \u300d\u3068\u3044\u3046\u4e26\u3073\u306b, \\(1\\) \u3092\u8ffd\u52a0\u3059\u308b\u65b9\u6cd5\u304c \\({} _ 4 \\text{C} {} _ 1 = 4\\) \u901a\u308a\u3042\u308a, \u305f\u3060\u3057 \\(( 1, 1, 2, 3 )\\) \u304c\u91cd\u8907\u3059\u308b\u306e\u3067\r\n\\[\r\n4 -1 = 3 \\ \\text{\u901a\u308a} \\ .\r\n\\]<\/li>\r\n
\r\n1*<\/strong>\u3068\u540c\u69d8\u306b\u8003\u3048\u3066\r\n\\[\r\n4 -1 = 3 \\ \\text{\u901a\u308a} \\ .\r\n\\]<\/li>\r\n
\r\n1*<\/strong>\u3068\u540c\u69d8\u306b\u8003\u3048\u3066\r\n\\[\r\n4 -1 = 3 \\ \\text{\u901a\u308a} \\ .\r\n\\]<\/li>\r\n<\/ol>\r\n
\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u5024\u306f\r\n\\[\r\ng(4) = 81 -3 \\cdot 3 = \\underline{72} \\ .\r\n\\]<\/li>\r\n<\/ul>\r\n\r\n
\r\n\\(\\text{C} {} _ 1\\) \u3092\u6e80\u305f\u3055\u306a\u3044 \\(S _ n\\) \u306e\u8981\u7d20\u306e\u500b\u6570\u3092 \\(d(n)\\) \u3068\u304a\u304f\u3068\r\n\\[\r\nd(n) = 2^n \\quad ... [1] \\ .\r\n\\]\r\n\u96c6\u5408 \\(S _ {n+1}\\) \u306e\u4e2d\u3067, \u6761\u4ef6 \\( \\text{C} {} _ {12}\\) \u3092\u6e80\u305f\u3055\u306a\u3044\u3082\u306e\u306e\u3046\u3061<\/p>\r\n\r\n
\r\n
\u3010 \u5225 \u89e3 \u3011<\/h2>\r\n
\r\n\\(S _ n\\) \u306e\u3046\u3061, \u6700\u3082\u5de6\u306b\u3042\u308b\uff08\u9805\u756a\u304c\u5c0f\u3055\u3044\uff09 \\(1\\) \u3092 \\(a _ k = 1 \\ ( 1 \\leqq k \\leqq n-1 )\\) \u3068\u3059\u308b.
\r\n\u3053\u306e\u3068\u304d<\/p>\r\n\r\n
\r\n\\(S _ n\\) \u306e\u3046\u3061, \u6700\u3082\u5de6\u306b\u3042\u308b \\(1\\) , \u3053\u308c\u3088\u308a\u3082\u53f3\u306b\u3042\u308b\u4e2d\u3067\u6700\u3082\u5de6\u306b\u3042\u308b \\(2\\) \u3092\u305d\u308c\u305e\u308c \\(a _ k = 1 , \\ a _ {\\ell} = 2 \\ ( 1 \\leqq k \\lt \\ell \\leqq n-1 )\\) \u3068\u3059\u308b.
\r\n\u3053\u306e\u3068\u304d<\/p>\r\n\r\n