A374822 Antichain-Chain Quilt Numbers: Square table of the number of ASM quilts of type A_2(j) x C_k read down antidiagonals, where C_k is the chain poset or rank k and A_2(j) is the rank 2 poset with a unique minimal and maximal element and j atoms

2, 4, 2, 8, 4, 7, 16, 8, 17, 16, 32, 16, 43, 46, 30, 64, 32, 113, 142, 100, 50, 128, 64, 307, 466, 366, 190, 77, 256, 128, 857, 1606, 1444, 806, 329, 112, 512, 256, 2443, 5746, 6030, 3718, 1589, 532, 156, 1024, 512, 7073, 21142, 26260, 18230, 8393, 2884, 816

Offset

1,1

Links

Table of n, a(n) for n=1..54.

Sara Billey and Matjaž Konvalinka, Generalized rank functions and quilts of alternating sign matrices, arXiv:2412.03236 [math.CO], 2024. See p. 33.

Formula

T(j,k) = Sum_{i=2..k} (k+1-i)*i^j for j>=1 and k>1.

T(j,1) = 2^j for all j>=1 and k=1.

Example

Array begins:
  2,  4,  8, ...
  2,  4,  8, ...
  7, 17, 43, ...
  ...

Crossrefs

Cf. A374819, A374820, A374821, A297622, A374824.

Sequence in context: A278531 A366279 A364297 * A370353 A095728 A279354

Adjacent sequences: A374819 A374820 A374821 * A374823 A374824 A374825

Keyword

nonn,tabl

Author

Sara Billey and Matjaz Konvalinka, Jul 21 2024

Status

approved