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A356265
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Triangle read by rows. The reduced triangle of the partition triangle of reducible permutations (A356264). T(n, k) for n >= 1 and 0 <= k < n.
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4
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0, 1, 0, 1, 2, 0, 1, 8, 2, 0, 1, 21, 25, 2, 0, 1, 49, 152, 55, 2, 0, 1, 106, 697, 670, 117, 2, 0, 1, 223, 2756, 5493, 2509, 243, 2, 0, 1, 459, 9966, 36105, 33669, 8838, 497, 2, 0, 1, 936, 34095, 206698, 342710, 184305, 29721, 1007, 2, 0
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OFFSET
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1,5
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LINKS
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EXAMPLE
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Triangle T(n, k) starts: [Row sums]
[1] [0] [0]
[2] [1, 0] [1]
[3] [1, 2, 0] [3]
[4] [1, 8, 2, 0] [11]
[5] [1, 21, 25, 2, 0] [49]
[6] [1, 49, 152, 55, 2, 0] [259]
[7] [1, 106, 697, 670, 117, 2, 0] [1593]
[8] [1, 223, 2756, 5493, 2509, 243, 2, 0] [11227]
[9] [1, 459, 9966, 36105, 33669, 8838, 497, 2, 0] [89537]
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PROG
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(SageMath) # uses function A356264_row
@cache
def Pn(n: int, k: int) -> int:
if k == 0: return 0
if n == 0 or k == 1: return 1
return Pn(n, k - 1) + Pn(n - k, k) if k <= n else Pn(n, k - 1)
def reduce_parts(fun, n: int) -> list[int]:
funn: list[int] = fun(n)
return [sum(funn[Pn(n, k):Pn(n, k + 1)]) for k in range(n)]
def reduce_partition_triangle(fun, n: int) -> list[list[int]]:
return [reduce_parts(fun, k) for k in range(1, n)]
def A356265_row(n: int) -> list[int]:
return reduce_partition_triangle(A356264_row, n+1)[n-1]
for n in range(1, 8):
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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