cp's OEIS Frontend

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.

%I A374822 #22 Jul 23 2025 16:05:50
%S A374822 2,4,2,8,4,7,16,8,17,16,32,16,43,46,30,64,32,113,142,100,50,128,64,
%T A374822 307,466,366,190,77,256,128,857,1606,1444,806,329,112,512,256,2443,
%U A374822 5746,6030,3718,1589,532,156,1024,512,7073,21142,26260,18230,8393,2884,816
%N 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.
%H A374822 Sara Billey and Matjaž Konvalinka, <a href="https://arxiv.org/abs/2412.03236">Generalized rank functions and quilts of alternating sign matrices</a>, arXiv:2412.03236 [math.CO], 2024. See p. 33.
%F A374822 T(j,k) = Sum_{i=2..k} (k+1-i)*i^j for j>=1 and k>1.
%F A374822 T(j,1) = 2^j for all j>=1 and k=1.
%e A374822 Array begins:
%e A374822   2,  4,  8, ...
%e A374822   2,  4,  8, ...
%e A374822   7, 17, 43, ...
%e A374822   ...
%Y A374822 Cf. A374819, A374820, A374821, A297622, A374824.
%K A374822 nonn,tabl
%O A374822 1,1
%A A374822 _Sara Billey_ and _Matjaz Konvalinka_, Jul 21 2024