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A356266
Partition triangle read by rows, counting reducible permutations with weakly decreasing Lehmer code, refining triangle A356115.
2
1, 1, 0, 1, 0, 1, 1, 0, 1, 2, 1, 1, 0, 1, 3, 3, 3, 3, 1, 0, 1, 4, 4, 2, 6, 12, 2, 4, 6, 1, 0, 1, 5, 5, 5, 10, 20, 10, 10, 10, 30, 10, 5, 10, 1, 0, 1, 6, 6, 6, 3, 15, 30, 30, 15, 15, 20, 60, 30, 60, 5, 15, 60, 30, 6, 15, 1
OFFSET
0,10
LINKS
Peter Luschny, Permutations with Lehmer, a SageMath Jupyter Notebook.
EXAMPLE
[0] 1;
[1] 1;
[2] 0, 1;
[3] 0, 1, 1;
[4] 0, [1, 2], 1, 1;
[5] 0, [1, 3], [3, 3], 3, 1;
[6] 0, [1, 4, 4], [2, 6, 12], [2, 4], 6, 1;
[7] 0, [1, 5, 5], [5, 10, 20, 10], [10, 10, 30], [10, 5], 10, 1;
[8] 0, [1, 6, 6, 6],[3,15, 30, 30, 15],[15, 20, 60, 30, 60],[5,15,60],[30,6],15,1;
Summing the bracketed terms reduces the triangle to A356115.
PROG
(SageMath) # uses functions perm_red_stats and reducible from A356264.
@cache
def A356266_row(n: int) -> list[int]:
if n < 2: return [1]
return [0] + [v[1] for v in perm_red_stats(n, reducible, weakly_decreasing)]
def A356266(n: int, k: int) -> int:
return A356266_row(n)[k]
for n in range(8):
print(A356266_row(n))
CROSSREFS
Cf. A356264, A356115 (reduced), A120588 (row sums).
Sequence in context: A342689 A077042 A144903 * A108934 A108947 A338859
KEYWORD
nonn,tabf
AUTHOR
Peter Luschny, Aug 16 2022
STATUS
approved