A356266 Partition triangle read by rows, counting reducible permutations with weakly decreasing Lehmer code, refining triangle A356115.

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

Table of n, a(n) for n=0..66.

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

Adjacent sequences: A356263 A356264 A356265 * A356267 A356268 A356269

Keyword

nonn,tabf

Author

Peter Luschny, Aug 16 2022

Status

approved