{"id":1930,"date":"2021-10-19T15:38:53","date_gmt":"2021-10-19T06:38:53","guid":{"rendered":"https:\/\/www.roundown.net\/nyushi\/?p=1930"},"modified":"2021-10-19T15:38:53","modified_gmt":"2021-10-19T06:38:53","slug":"wsr201601","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/wsr201601\/","title":{"rendered":"\u65e9\u7a32\u7530\u7406\u5de52016\uff1a\u7b2c1\u554f"},"content":{"rendered":"
\n

\u6b63\u306e\u5b9f\u6570 \\(m , n\\) \u306b\u5bfe\u3057\u3066 \\(f( m , n )\\) \u304c\u6b21\u306e\u7b49\u5f0f\u3092\u6e80\u305f\u3059\u3088\u3046\u306b\u5b9a\u3081\u3089\u308c\u3066\u3044\u308b.\r\n\\[\r\n\\left\\{ \\begin{array}{l} f( 1 , 1 ) = 1 , \\ f( 2 , 2 ) = 6 , \\ f( 3 ,3 ) = 20 \\\\ f( m , n ) = 2 f( m-1 , n ) \\quad ( m \\geqq 2 )\\\\ f( m , n ) +3 f( m , n-2 ) = 3 f( m , n-1 ) +f( m , n-3 ) \\quad ( n \\geqq 4 )\\end{array} \\right.\r\n\\]\r\n\u6b21\u306e\u554f\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(f( m , 1 )\\) \u304a\u3088\u3073 \\(f( 1 , n )\\) \u3092\u305d\u308c\u305e\u308c \\(m , n\\) \u306e\u5f0f\u3067\u8868\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(f( 6 , 32 )\\) \u306e\u5024\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\u4efb\u610f\u306e\u6b63\u306e\u6574\u6570 \\(l\\) \u306b\u5bfe\u3057\u3066, \\(f( m , n ) = l\\) \u3092\u6e80\u305f\u3059\u6b63\u306e\u6574\u6570 \\(m , n\\) \u304c\u5b58\u5728\u3059\u308b\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n

    (1)<\/strong><\/p>\r\n

    \u4e0e\u3048\u3089\u308c\u305f\u5f0f\u3092\u9806\u306b [1] \uff5e [5] \u3068\u3059\u308b.
    \r\n[1] [4] \u3088\u308a, \u6570\u5217 \\(\\{ f( m , 1 ) \\}\\) \u306f, \u521d\u9805 \\(f( 1 , 1 ) = 1\\) , \u516c\u6bd4 \\(2\\) \u306e\u7b49\u6bd4\u6570\u5217\u306a\u306e\u3067\r\n\\[\r\nf( m , 1 ) = \\underline{2^{m-1}}\r\n\\]\r\n[2] [3] \u306b [4] \u3092\u7528\u3044\u308c\u3070\r\n\\[\\begin{align}\r\nf( 1 , 2 ) & = \\dfrac{1}{2} \\cdot 6 = 3 \\quad ... [6] \\ , \\\\\r\nf( 2 , 3 ) & = \\dfrac{1}{2} \\cdot 20 = 10 \\ , \\\\\r\nf( 1 , 3 ) & = \\dfrac{1}{2} \\cdot 10 = 5 \\quad ... [7]\r\n\\end{align}\\]\r\n\u4ee5\u4e0b\u3067\u306f, \\(f( 1 , n ) = 2n-1\\) ... [A] \u3067\u3042\u308b\u3053\u3068\u3092, \u6570\u5b66\u7684\u5e30\u7d0d\u6cd5\u3092\u7528\u3044\u3066\u793a\u3059.<\/p>\r\n

      \r\n

    1. 1*<\/strong>\u3000\\(n = 1 , 2 , 3\\) \u306e\u3068\u304d
      \r\n[1] [6] [7] \u3088\u308a, [A] \u304c\u6210\u7acb\u3057\u3066\u3044\u308b.<\/p><\/li>\r\n

    2. 2*<\/strong>\u3000\\(n= k , k+1 , k+2\\) \u306e\u3068\u304d, [A] \u304c\u6210\u7acb\u3059\u308b, \u3059\u306a\u308f\u3061\r\n\\[\r\nf( 1 , k ) = 2k-1 , \\ f( 1 , k+1 ) = 2k+1 , \\ f( 1 , k+2 ) = 2k+3\r\n\\]\r\n\u3068\u4eee\u5b9a\u3059\u308b\u3068, [5] \u3088\u308a\r\n\\[\\begin{align}\r\nf( 1 , k+3 ) & = 3 f( 1 , k+2 ) +f( 1 , k ) -3 f( 1 , k+1 ) \\\\\r\n& = 3 ( 2k+3 ) +2k-1 -3 ( 2k+1 ) \\\\\r\n& = 2 ( k+3 ) -1\r\n\\end{align}\\]\r\n\u306a\u306e\u3067, \\(n = k+3\\) \u306e\u3068\u304d\u3082 [A] \u304c\u6210\u7acb\u3059\u308b.<\/p><\/li>\r\n<\/ol>\r\n

      \u4ee5\u4e0a\u3088\u308a, \u3059\u3079\u3066\u306e\u81ea\u7136\u6570 \\(n\\) \u3067 [A] \u304c\u6210\u7acb\u3057\r\n\\[\r\nf( 1 , n ) = \\underline{2n-1}\r\n\\]\r\n

      (2)<\/strong><\/p>\r\n

      (1)<\/strong> \u306e\u7d50\u679c\u306b, \u518d\u5ea6 [4] \u3092\u7528\u3044\u308c\u3070, \u6570\u5217 \\(\\{ f( m , n ) \\}\\) \u306f, \u521d\u9805 \\(f( 1 , n ) = 2n-1\\) , \u516c\u6bd4 \\(2\\) \u306e\u7b49\u6bd4\u6570\u5217\u306a\u306e\u3067\r\n\\[\r\nf( m , n ) = 2^{m-1} ( 2n-1 ) \\quad ... [8]\r\n\\]\r\n\u3088\u3063\u3066\r\n\\[\\begin{align}\r\nf( 6 , 32 ) & = 2^5 \\cdot 63 = 2^5 \\left( 2^6 -1 \\right) \\\\\r\n& = 2048 -32 = \\underline{2016}\r\n\\end{align}\\]\r\n

      (3)<\/strong><\/p>\r\n

      \\(l\\) \u3092\u7d20\u56e0\u6570\u5206\u89e3\u3059\u308b\u3053\u3068\u3092\u8003\u3048\u308c\u3070, \\(0\\) \u4ee5\u4e0a\u306e\u6574\u6570 \\(p\\) \u3068\u5947\u6570 \\(Q\\) \u3092\u7528\u3044\u3066\r\n\\[\r\nl = 2^p Q\r\n\\]\r\n\u3068\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b.
      \r\n[8] \u3088\u308a, \\(m = p+1\\) , \\(n = \\dfrac{Q+1}{2}\\) \u3068\u3059\u308c\u3070, \\(f( m , n ) = l\\) \u3068\u306a\u308a, \u984c\u610f\u306f\u793a\u3055\u308c\u305f.<\/p>\r\n","protected":false},"excerpt":{"rendered":"\u6b63\u306e\u5b9f\u6570 \\(m , n\\) \u306b\u5bfe\u3057\u3066 \\(f( m , n )\\) \u304c\u6b21\u306e\u7b49\u5f0f\u3092\u6e80\u305f\u3059\u3088\u3046\u306b\u5b9a\u3081\u3089\u308c\u3066\u3044\u308b. \\[ \\left\\{ \\begin{array}{l} f( 1 , 1 ) = 1 , \\ f( 2 , … \u7d9a\u304d\u3092\u8aad\u3080 →<\/span><\/a>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[157],"tags":[147,162],"class_list":["post-1930","post","type-post","status-publish","format-standard","hentry","category-waseda_r_2016","tag-waseda_r","tag-162"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1930","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/comments?post=1930"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1930\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1930"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1930"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1930"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}