{"id":1257,"date":"2015-08-27T10:04:02","date_gmt":"2015-08-27T01:04:02","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1257"},"modified":"2021-09-08T20:49:57","modified_gmt":"2021-09-08T11:49:57","slug":"osr201505","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/osr201505\/","title":{"rendered":"\u962a\u5927\u7406\u7cfb2015\uff1a\u7b2c5\u554f"},"content":{"rendered":"<hr \/>\n<p>\\(n\\) \u3092 \\(2\\) \u4ee5\u4e0a\u306e\u6574\u6570\u3068\u3059\u308b.\r\n\u6b63\u65b9\u5f62\u306e\u5f62\u306b\u4e26\u3093\u3060 \\(n \\times n\\) \u306e\u30de\u30b9\u306b \\(0\\) \u307e\u305f\u306f \\(1\\) \u306e\u3044\u305a\u308c\u304b\u306e\u6570\u5b57\u3092\u5165\u308c\u308b. \u30de\u30b9\u306f\u4e0a\u304b\u3089\u7b2c \\(1\\) \u884c, \u7b2c \\(2\\) \u884c, \u2026 , \u5de6\u304b\u3089\u7b2c \\(1\\) \u5217, \u7b2c \\(2\\) \u5217, \u2026 , \u3068\u6570\u3048\u308b.\r\n\u6570\u5b57\u306e\u5165\u308c\u65b9\u306b\u3064\u3044\u3066\u306e\u6b21\u306e\u6761\u4ef6 \\(p\\) \u3092\u8003\u3048\u308b.<\/p>\r\n<ol>\r\n<li>\u6761\u4ef6 \\(p\\) \uff1a \\(1\\) \u304b\u3089 \\(n-1\\) \u307e\u3067\u306e\u3069\u306e\u6574\u6570 \\(i , j\\) \u306b\u3064\u3044\u3066\u3082, \u7b2c \\(i\\) \u884c, \u7b2c \\(i+1\\) \u884c\u3068\u7b2c \\(j\\) \u5217, \u7b2c \\(j+1\\) \u5217\u3068\u304c\u4f5c\u308b \\(2 \\times 2\\) \u306e \\(4\\) \u30de\u30b9\u306b\u306f \\(0\\) \u3068 \\(1\\) \u304c \\(2\\) \u3064\u305a\u3064\u5165\u308b.<\/li>\r\n<\/ol>\r\n<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\u6761\u4ef6 \\(p\\) \u3092\u6e80\u305f\u3059\u3068\u304d, \u7b2c \\(n\\) \u884c\u3068\u7b2c \\(n\\) \u5217\u306e\u5c11\u306a\u304f\u3068\u3082\u4e00\u65b9\u306b\u306f \\(0\\) \u3068 \\(1\\) \u304c\u4ea4\u4e92\u306b\u73fe\u308c\u308b\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000\u6761\u4ef6 \\(p\\) \u3092\u6e80\u305f\u3059\u3088\u3046\u306a\u6570\u5b57\u306e\u5165\u308c\u65b9\u306e\u7dcf\u6570 \\(a _ n\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/osr20150501.svg\" alt=\"osr20150501\" class=\"aligncenter size-full wp-image-1258\" \/>\r\n<hr \/>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<p>\u6761\u4ef6 \\(p\\) \u3092\u307f\u305f\u3059\u6570\u5b57\u306e\u5165\u308c\u65b9\u306b\u3064\u3044\u3066, \\(2 \\times 2\\) \u306e \\(4\\) \u30de\u30b9\u306e\u3046\u3061<\/p>\r\n<ol>\r\n<li>[1] \uff1a \\(3\\) \u30de\u30b9\u306e\u6570\u5b57\u304c\u6c7a\u307e\u3063\u3066\u3044\u308c\u3070\uff08\u3059\u3079\u3066\u540c\u3058\u6570\u5b57\u306e\u5834\u5408\u306f\u9664\u304f\uff09, \u6b8b\u308a \\(1\\) \u30de\u30b9\u306b\u5165\u308b\u6570\u5b57\u306f, \u4e00\u610f\u306b\u6c7a\u307e\u308b.<\/p><\/li>\r\n<li>[2] \uff1a \u96a3\u308a\u5408\u3046 \\(2\\) \u30de\u30b9\u306b\u540c\u3058\u6570\u5b57\u304c\u5165\u3063\u3066\u3044\u308c\u3070, \u6b8b\u308a \\(2\\) \u30de\u30b9\u306b\u5165\u308b\u6570\u5b57\u306f, \u3053\u308c\u3068\u7570\u306a\u308b\u6570\u5b57\u306b\u4e00\u610f\u306b\u6c7a\u307e\u308b.<\/p><\/li>\r\n<\/ol>\r\n<p>\u307e\u305f, \u7b2c \\(n\\) \u884c\uff08\u5217\uff09\u306b \\(0 , 1\\) \u304c\u4ea4\u4e92\u306b\u73fe\u308c\u3066\u3044\u308b\u3053\u3068\u3092, \u300c\u7b2c \\(n\\) \u884c\uff08\u5217\uff09\u304c\u4ea4\u4e92\u3067\u3042\u308b\u300d\u3068\u3088\u3076\u3053\u3068\u3068\u3059\u308b.<\/p>\r\n<p><strong>(1)<\/strong><\/p>\r\n<p>\u80cc\u7406\u6cd5\u3092\u7528\u3044\u3066\u793a\u3059.<br \/>\r\n\u7b2c \\(n\\) \u884c , \u7b2c \\(n\\) \u5217\u3068\u3082\u306b \u4ea4\u4e92\u3067\u306a\u3044, \u3068\u4eee\u5b9a\u3059\u308b.<\/p>\r\n<ol>\r\n<li>[3] \uff1a \u7b2c \\(n\\) \u5217\u306e\u7b2c \\(i\\) \u884c, \u7b2c \\(i+1\\) \u884c\u304c\u540c\u3058\u6570\u5b57\u3067\u3042\u308c\u3070, \u7b2c \\(i\\) \u884c\u3068\u7b2c \\(i+1\\) \u884c\u306f\u3068\u3082\u306b\u4ea4\u4e92\u3067\u3042\u308b.<\/p><\/li>\r\n<li>[4] \uff1a \u7b2c \\(n\\) \u884c\u306e\u7b2c \\(j\\) \u5217, \u7b2c \\(j+1\\) \u5217\u304c\u540c\u3058\u6570\u5b57\u3067\u3042\u308c\u3070, \u7b2c \\(j\\) \u5217\u3068\u7b2c \\(j+1\\) \u5217\u306f\u3068\u3082\u306b\u4ea4\u4e92\u3067\u3042\u308b.<\/p><\/li>\r\n<\/ol>\r\n<p>\u3057\u304b\u3057, \u7b2c \\(i\\) \u884c, \u7b2c \\(i+1\\) \u884c\u3068, \u7b2c \\(j\\) \u5217, \u7b2c \\(j+1\\) \u5217\u304c\u4ea4\u5dee\u3059\u308b \\(2 \\times 2\\) \u306e \\(4\\) \u30de\u30b9\u306b\u7740\u76ee\u3059\u308c\u3070, [3] \u3068 [4] \u304c\u540c\u6642\u306b\u6210\u7acb\u3059\u308b\u3053\u3068\u306f\u306a\u3044\u306e\u3067, \u77db\u76fe\u3059\u308b.<br \/>\r\n\u3088\u3063\u3066, \u984c\u610f\u306f\u793a\u3055\u308c\u305f.<\/p>\r\n<p><strong>(2)<\/strong><\/p>\r\n<p>\\(n \\times n\\) \u306e\u30de\u30b9\u306e\u3046\u3061, \u7b2c \\(n\\) \u884c\u3068\u7b2c \\(n\\) \u5217\u304c\u3068\u3082\u306b\u4ea4\u4e92\u3067\u3042\u308b\u3082\u306e\u3092\u4e21\u4ea4\u4e92, \u4e00\u65b9\u306e\u307f\u304c\u4ea4\u4e92\u3067\u3042\u308b\u3082\u306e\u3092\u7247\u4ea4\u4e92\u3068\u3088\u3076\u3053\u3068\u3068\u3059\u308b.<br \/>\r\n\\(n \\times n\\) \u306e\u30de\u30b9\u306e\u3046\u3061, \u4e21\u4ea4\u4e92\u3067\u3042\u308b\u500b\u6570\u3092 \\(b _ n\\) , \u7247\u4ea4\u4e92\u3067\u3042\u308b\u500b\u6570\u3092 \\(c _ n\\) \u3068\u304a\u304f\u3068<br \/>\r\n\\[\r\nb _ 2 = 2 , \\ c _ 2 = 4 \\quad ... [5] \\ .\r\n\\]\r\n\u7b2c \\(n\\) \u884c\u306e\u96a3\u308a\u306b\u7b2c \\(n+1\\) \u884c\u3092\u8ffd\u52a0\u3059\u308b\u3068\u304d, [1] [2] \u306b\u6ce8\u610f\u3059\u308c\u3070<\/p>\r\n<ol>\r\n<li>[6] \uff1a \u7b2c \\(n\\) \u884c\u304c\u4ea4\u4e92\u3067\u3042\u308c\u3070, \u7b2c \\(n+1\\) \u884c\u306e\u6570\u5b57\u306e\u5165\u308c\u65b9\u306f \\(2\\) \u901a\u308a\uff08\u7b2c \\(n\\) \u884c\u3068\u540c\u3058\u6570\u5b57\u304b\u3068\u7570\u306a\u308b\u6570\u5b57\u3092\u5165\u308c\u308b\uff09\u3042\u308a, \u3069\u3061\u3089\u3082\u4ea4\u4e92\u3067\u3042\u308b.<\/p><\/li>\r\n<li>[7] \uff1a \u7b2c \\(n\\) \u884c\u304c\u4ea4\u4e92\u3067\u306a\u3051\u308c\u3070, \u7b2c \\(n+1\\) \u884c\u306e\u6570\u5b57\u306e\u5165\u308c\u65b9\u306f \\(1\\) \u901a\u308a\u306e\u307f\uff08\u7b2c \\(n\\) \u884c\u3068\u7570\u306a\u308b\u6570\u5b57\u3092\u5165\u308c\u308b\uff09\u3067, \u4ea4\u4e92\u3067\u306f\u306a\u3044.<\/p><\/li>\r\n<\/ol>\r\n<p>\uff08 [6] [7] \u306f\u300c\u884c\u300d\u3092\u300c\u5217\u300d\u306b\u8a00\u3044\u63db\u3048\u3066\u3082\u540c\u69d8\u306b\u6210\u308a\u7acb\u3064. \uff09<br \/>\r\n\\(n \\times n\\) \u306e\u30de\u30b9\u306b, \u7b2c \\(n+1\\) \u884c\u3068\u7b2c \\(n+1\\) \u5217\u3092\u52a0\u3048\u3066, \\((n+1) \\times (n+1)\\) \u306e\u30de\u30b9\u3092\u4f5c\u308b\u3053\u3068\u3092\u8003\u3048\u308b.<br \/>\r\n\u3053\u306e\u3068\u304d<\/p>\r\n<ol>\r\n<li><p><strong>1*<\/strong>\u3000\\(n \\times n\\) \u306e\u30de\u30b9\u304c\u7247\u4ea4\u4e92\u306e\u3068\u304d\uff08\u7b2c \\(n\\) \u884c\u304c\u4ea4\u4e92\u3068\u3059\u308b\uff09<br \/>\r\n\u7b2c \\(n+1\\) \u5217\u306e\u7b2c \\(1, 2, \\cdots , n\\) \u884c\u306e\u6570\u5b57\u306e\u5165\u308c\u65b9\u306f, [7] \u3088\u308a \\(1\\) \u901a\u308a\u306e\u307f.<br \/>\r\n\u305d\u306e\u5f8c, \u7b2c \\(n+1\\) \u884c\u306e\u7b2c \\(1, 2, \\cdots , n+1\\) \u5217\u306e\u6570\u5b57\u306e\u5165\u308c\u65b9\u306f, [6] \u3088\u308a \\(2\\) \u901a\u308a.<br \/>\r\n\u3057\u305f\u304c\u3063\u3066, \\((n+1) \\times (n+1)\\) \u306e\u30de\u30b9\u306f \\(2\\) \u901a\u308a\u3042\u308a, \u3044\u305a\u308c\u3082\u7247\u4ea4\u4e92\u3067\u3042\u308b.<\/p><\/li>\r\n<li><p><strong>2*<\/strong>\u3000\\(n \\times n\\) \u306e\u30de\u30b9\u304c\u4e21\u4ea4\u4e92\u306e\u3068\u304d<br \/>\r\n\u7b2c \\(n+1\\) \u884c\uff08\u5217\uff09\u306e\u7b2c \\(1, 2, \\cdots , n\\) \u5217\uff08\u884c\uff09\u306e\u6570\u5b57\u306e\u5165\u308c\u65b9\u306f, [6] \u3088\u308a\u305d\u308c\u305e\u308c \\(2\\) \u901a\u308a\u305a\u3064.<br \/>\r\n\u6700\u5f8c\u306b, \u7b2c \\(n+1\\) \u884c\u306e\u7b2c \\(n+1\\) \u5217\u304c [1] \u306b\u3088\u3063\u3066\u6c7a\u307e\u308a,\r\n\u7b2c \\(n+1\\) \u884c\uff08\u5217\uff09\u3092\u7b2c \\(n\\) \u884c\uff08\u5217\uff09\u3068\u540c\u3058\u6570\u5b57\u3042\u308b\u3044\u306f\u7570\u306a\u308b\u6570\u5b57\u306b\u3059\u308b\u304b\u306b\u5fdc\u3058\u3066, \\((n+1) \\times (n+1)\\) \u306e\u30de\u30b9\u306f, \u4e0b\u8868\u306e\u3088\u3046\u306b \\(3\\) \u901a\u308a\u3042\u308a, \\(1\\) \u3064\u306f\u4e21\u4ea4\u4e92, \\(2\\) \u3064\u306f\u7247\u4ea4\u4e92\u3067\u3042\u308b.<br \/>\r\n\\[\r\n\\begin{array}{c|c|c} \\text{\u884c\uff3c\u5217} & \\text{\u540c\u3058\u6570\u5b57} & \\text{\u7570\u306a\u308b\u6570\u5b57} \\\\ \\hline \\text{\u540c\u3058\u6570\u5b57} & \\text{\u4e21\u4ea4\u4e92} & \\text{\u7247\u4ea4\u4e92} \\\\ \\hline \\text{\u7570\u306a\u308b\u6570\u5b57} & \\text{\u7247\u4ea4\u4e92} & \\text{\u00d7} \\end{array}\r\n\\]\r\n\uff08\u3053\u3053\u3067, \u3068\u3082\u306b\u540c\u3058\u6570\u5b57\u3092\u5165\u308c\u305f\u5834\u5408\u306f, \u6761\u4ef6 \\(p\\) \u306b\u53cd\u3059\u308b\u70b9\u306b\u6ce8\u610f\u3059\u308b. \uff09<\/p><\/li>\r\n<\/ol>\r\n<p>\u4ee5\u4e0a\u3088\u308a\r\n\\[\r\n\\left\\{ \\begin{array}{ll} b _ {n+1} = b _ n & ... [8] \\\\ c _ {n+1} = 2 c _ n +2 b _ n & ... [9] \\end{array} \\right. \\ .\r\n\\]\r\n[5] [8] \u3088\u308a\r\n\\[\r\nb _ n = 2 \\ .\r\n\\]\r\n[9] \u306b\u4ee3\u5165\u3059\u308c\u3070\r\n\\[\\begin{align}\r\nc _ {n+1} & = 2 c _ n +4 \\\\\r\n\\text{\u2234} \\quad c _ {n+1} +4 & = 2 ( c _ n +4 ) \\ .\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, [5] \u3082\u7528\u3044\u3066\r\n\\[\\begin{align}\r\nc _ n +4 & = (4+4) \\cdot 2^{n-2} = 2^{n+1} \\\\\r\n\\text{\u2234} & \\quad c _ n = 2^{n+1} -4 \\ .\r\n\\end{align}\\]\r\n\u3088\u3063\u3066\r\n\\[\r\na _ n = b _ n +c _ n = \\underline{2^{n+1} -2} \\ .\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(n\\) \u3092 \\(2\\) \u4ee5\u4e0a\u306e\u6574\u6570\u3068\u3059\u308b. \u6b63\u65b9\u5f62\u306e\u5f62\u306b\u4e26\u3093\u3060 \\(n \\times n\\) \u306e\u30de\u30b9\u306b \\(0\\) \u307e\u305f\u306f \\(1\\) \u306e\u3044\u305a\u308c\u304b\u306e\u6570\u5b57\u3092\u5165\u308c\u308b. \u30de\u30b9\u306f\u4e0a\u304b\u3089\u7b2c \\(1\\) \u884c, \u7b2c \\(2\\) \u884c &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/osr201505\/\">\u7d9a\u304d\u3092\u8aad\u3080 <span class=\"meta-nav\">&rarr;<\/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":[127],"tags":[142,137],"class_list":["post-1257","post","type-post","status-publish","format-standard","hentry","category-osaka_r_2015","tag-osaka_r","tag-137"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1257","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=1257"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1257\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1257"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1257"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1257"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}