Re: [理工] [離散]-生成函數
※ 引述《assassin88 (Ace)》之銘言：
: Determine how many integer solutions there are to x1+x2+x3+x4=18 if 0<=xi<=7
: for all 1<=i<=4 and both x2 and x4 are odd.
: 想請問的是有沒有特別解法，因為如果生成函數解很麻煩..
(1+x+x^2+...)^2(x+x^3+x^5+x^7)^2
= x^2(1-x^8/1-x)^2(1-x^8/1-x^2)^2
= x^2(1-x^8)^4(1-x)^-2(1-x^2)^-2
= x^2(1-x^8)^4(1-x)^-4(1+x)^-2
= x^2(1-4x^8+6x^16-...)Σ(4+r-1)x^rΣ(-1)^r(2+r-1)x^r
r r
= (4+8-1)(2+8-1) - 4(4+4-1)(2+4-1) + 6
8 8 4 4
想請問這樣為什麼不行
我有少哪些想法嗎
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◆ From: 124.8.1.138
推
03/02 11:07, , 1F
03/02 11:07, 1F
→
03/02 11:08, , 2F
03/02 11:08, 2F
→
03/02 11:15, , 3F
03/02 11:15, 3F
推
03/02 11:17, , 4F
03/02 11:17, 4F
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03/02 11:19, , 5F
03/02 11:19, 5F
推
03/02 11:28, , 6F
03/02 11:28, 6F
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03/02 11:34, , 7F
03/02 11:34, 7F
※ 編輯: supergud 來自: 124.8.1.138 (03/02 12:02)
推
03/02 15:00, , 8F
03/02 15:00, 8F
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