三角形面积公式

王守恩

northwolves 发表于 2024-7-6 13:18
以7为例：

以7为例：OEIS有这串数, 没我们这种说法。没我们这种简单的说法
以3为例：OEIS没有了。我们这种说法不是挺简单的吗？
n个苹果，分成4,5,6,...堆。
你好像都有方法(我还是领会不了)。

王守恩

1. Table[CoefficientList[Series[(Prod_{k=a}^{2a}(1 - x^k))^{-1}, {x, 0, 49}], x], {a, 1, 8}]

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n个苹果, 分成2堆。{1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19,  20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25},
n个苹果, 分成3堆。{1, 0, 1, 1, 2, 1, 3, 2, 4, 3, 5, 4, 7, 5, 8, 7, 10, 8, 12, 10, 14, 12, 16, 14, 19, 16, 21, 19, 24, 21, 27, 24, 30, 27, 33, 30, 37, 33, 40, 37, 44, 40, 48,44, 52, 48, 56, 52, 61, 56},
n个苹果, 分成4堆。{1, 0, 0, 1, 1, 1, 2, 1, 2, 3, 3, 3, 5, 4, 5, 7, 7, 7, 10, 9, 11, 13, 13, 14, 18, 17, 19, 22, 23, 24, 29, 28, 31, 35, 36, 38, 44, 43, 47, 52, 54, 56, 63, 63, 68, 74, 76, 79, 88, 88},
n个苹果, 分成5堆。{1, 0, 0, 0, 1, 1, 1, 1, 2, 1, 2, 2, 4, 3, 4, 4, 6, 5, 7, 7, 10, 9, 11, 11, 15, 14, 17, 17, 22, 21, 25, 25, 31, 30, 35, 36, 43, 42, 48, 49, 58, 57, 65, 66, 76, 76, 85, 87, 99, 99},
n个苹果, 分成6堆。{1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 1, 2, 2, 3, 4, 4, 4, 5, 5, 7, 7, 8, 9, 11, 12, 13, 14, 16, 17, 21, 21, 24, 26, 29, 32, 35, 37, 41, 44, 50, 52, 58, 61, 67, 73, 78, 83, 91, 96},
n个苹果, 分成7堆。{1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 3, 3, 5, 4, 5, 5, 6, 6, 9, 8, 10, 11, 13, 13, 17, 16, 19, 20, 23, 24, 30, 29, 34, 36, 41, 42, 50, 50, 57, 60, 67, 70, 81, 82},
n个苹果, 分成8堆。{1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 3, 3, 4, 5, 5, 5, 6, 6, 7, 8, 10, 10, 12, 13, 15, 16, 18, 20, 22, 23, 26, 28, 32, 34, 39, 41, 46, 49, 54, 58, 64, 69},
n个苹果, 分成9堆。{1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 3, 3, 4, 4, 6, 5, 6, 6, 7, 7, 9, 9, 12, 12, 14, 15, 18, 18, 21, 22, 26, 26, 30, 31, 36, 38, 43, 45, 53, 54},

王守恩

northwolves 发表于 2024-7-6 13:18
以7为例：

继续讨教。把2024个苹果分成5堆, 最小的一堆不小于224, 最大的一堆不大于另3堆(较小)的和, 这样的分法有多少种？