Puzzleup 2016 (5) ONE HUNDRED COINS - 拼圖

題目網址: http://www.puzzleup.com/2016/
http://www.puzzleup.com/2016/puzzle/?5
答題時限: ８月25日７ＰＭ－比賽結束（約12月14日）
加分時限: ８月25日７ＰＭ－８月30日６：５９ＰＭ

答對可得基本分１００分。答案可上傳５次，每改１次答案從基本分扣２０分。　
比賽期間內可隨時上傳答案，加分時限內答對第ｎ天加（６－ｎ）分　 　　 　　
另依題目的難易有額外加分（如有８０％的人這題答錯，答對者加８０分）　　

◆ONE HUNDRED COINS

In how many ways 100 gold coins can be divided into groups, so that the
difference between any two groups is at most 2?

Note: Permutations are not considered as different.

Example: If the problem was asked for 6 coins, the answer would be 9:
(1,1,1,1,1,1), (1,1,1,1,2), (1,1,2,2), (1,1,1,3), (1,2,3), (2,2,2), (2,4),
(3,3), (6).

現要把一百枚金幣分成數堆，使得任意兩堆的金幣數都最多差２，有幾種方法？

# 重新排列並不視為不同的方法


舉例: 6個金幣有9種分法:
(1,1,1,1,1,1), (1,1,1,1,2), (1,1,2,2), (1,1,1,3), (1,2,3), (2,2,2), (2,4),
(3,3), (6).

--