{"id":426,"date":"2012-06-14T23:42:13","date_gmt":"2012-06-14T14:42:13","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=426"},"modified":"2021-10-20T14:55:20","modified_gmt":"2021-10-20T05:55:20","slug":"ykr201203","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/ykr201203\/","title":{"rendered":"\u6a2a\u56fd\u5927\u7406\u7cfb2012\uff1a\u7b2c3\u554f"},"content":{"rendered":"
\n

\u6b21\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(k\\) \u3092 \\(0\\) \u4ee5\u4e0a\u306e\u6574\u6570\u3068\u3059\u308b\u3068\u304d,\r\n\\[\r\n\\dfrac{x}{3} +\\dfrac{y}{2} \\leqq k\r\n\\]\r\n\u3092\u6e80\u305f\u3059 \\(0\\) \u4ee5\u4e0a\u306e\u6574\u6570 \\(x , y\\) \u306e\u7d44 \\((x,y)\\) \u306e\u500b\u6570\u3092 \\(a _ k\\) \u3068\u3059\u308b. \\(a _ k\\) \u3092 \\(k\\) \u306e\u5f0f\u3067\u8868\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(n\\) \u3092 \\(0\\) \u4ee5\u4e0a\u306e\u6574\u6570\u3068\u3059\u308b\u3068\u304d,\r\n\\[\r\n\\dfrac{x}{3} +\\dfrac{y}{2} +z \\leqq n\r\n\\]\r\n\u3092\u6e80\u305f\u3059 \\(0\\) \u4ee5\u4e0a\u306e\u6574\u6570 \\(x , y , z\\) \u306e\u7d44 \\((x,y,z)\\) \u306e\u500b\u6570\u3092 \\(b _ n\\) \u3068\u3059\u308b. \\(b _ n\\) \u3092 \\(n\\) \u306e\u5f0f\u3067\u8868\u305b.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

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

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

    \\(\\ell\\) \u306f\u6574\u6570\u3068\u3059\u308b.<\/p>\r\n

      \r\n

    1. 1*<\/strong>\u3000\\(y =2 \\ell \\ ( 0 \\leqq \\ell \\leqq k )\\) \u306e\u3068\u304d\r\n\\[\\begin{align}\r\n\\dfrac{x}{3} +\\ell & \\leqq k \\\\\r\n\\text{\u2234} \\quad 0 \\leqq x & \\leqq 3( k-\\ell )\r\n\\end{align}\\]\r\n\u3053\u308c\u3092\u307f\u305f\u3059 \\(x\\) \u306e\u500b\u6570\u306f \\(3( k-\\ell ) +1\\) \u500b.<\/p><\/li>\r\n

    2. 2*<\/strong>\u3000\\(y =2 \\ell +1 \\ ( 0 \\leqq \\ell \\leqq k-1 )\\) \u306e\u3068\u304d\r\n\\[\\begin{align}\r\n\\dfrac{x}{3} +\\ell +\\dfrac{1}{2} & \\leqq k \\\\\r\n\\text{\u2234} \\quad 0 \\leqq x & \\leqq 3( k-\\ell ) -\\dfrac{3}{2}\r\n\\end{align}\\]\r\n\u3053\u308c\u3092\u307f\u305f\u3059 \\(x\\) \u306e\u500b\u6570\u306f \\(3( k-\\ell ) -1\\) \u500b.<\/p><\/li>\r\n<\/ol>\r\n

      \u4ee5\u4e0a\u3088\u308a\r\n\\[\\begin{align}\r\na _ k & = \\textstyle\\sum\\limits _ {\\ell =0}^{k} \\left\\{ 3( k-\\ell ) +1 \\right\\} +\\textstyle\\sum\\limits _ {\\ell =0}^{k-1} \\left\\{ 3( k-\\ell ) -1 \\right\\} \\\\\r\n& = \\textstyle\\sum\\limits _ {\\ell =1}^{k} 3 \\ell +(k+1) +\\textstyle\\sum\\limits _ {\\ell =1}^{k} 3 \\ell -k \\\\\r\n& = 6 \\cdot \\dfrac{k(k+1)}{2} +1 \\\\\r\n& =\\underline{3k^2+3k+1}\r\n\\end{align}\\]\r\n

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

      \\(0 \\leqq z \\leqq n\\) \u3067\u3042\u308a\r\n\\[\r\n\\dfrac{x}{3} +\\dfrac{y}{2} \\leqq n-z\r\n\\]\r\n\u306a\u306e\u3067, (1)<\/strong> \u306e\u7d50\u679c\u3092\u7528\u3044\u3066\r\n\\[\\begin{align}\r\nb _ n & = \\textstyle\\sum\\limits _ {z=0}^{n} a _ {n-z} = \\textstyle\\sum\\limits _ {z=0}^{n} a _ {z} \\\\\r\n& = \\textstyle\\sum\\limits _ {z=0}^{n} \\left\\{ (z+1)^3 -z^3 \\right\\} \\\\\r\n& = (n+1)^3 -n^3 +n^3 -(n-1)^3 +\\cdots +1^3 -0^3 \\\\\r\n& = \\underline{(n+1)^3}\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\u6b21\u306e\u554f\u3044\u306b\u7b54\u3048\u3088. (1)\u3000\\(k\\) \u3092 \\(0\\) \u4ee5\u4e0a\u306e\u6574\u6570\u3068\u3059\u308b\u3068\u304d, \\[ \\dfrac{x}{3} +\\dfrac{y}{2} \\leqq k \\] \u3092\u6e80\u305f\u3059 \\(0\\) \u4ee5\u4e0a\u306e\u6574\u6570 \\(x , y\\) \u306e\u7d44 … \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":[66],"tags":[68,9],"class_list":["post-426","post","type-post","status-publish","format-standard","hentry","category-yokokoku_r_2012","tag-68","tag-yokokoku_r"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/426","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=426"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/426\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=426"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=426"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=426"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}