A334548 Array read by antidiagonals: T(n,k) is the number of n X n symmetric binary matrices with no row sum greater than k.
1, 1, 1, 1, 2, 1, 1, 2, 5, 1, 1, 2, 8, 14, 1, 1, 2, 8, 45, 43, 1, 1, 2, 8, 64, 315, 142, 1, 1, 2, 8, 64, 809, 2634, 499, 1, 1, 2, 8, 64, 1024, 13846, 25518, 1850, 1, 1, 2, 8, 64, 1024, 28217, 301262, 280257, 7193, 1, 1, 2, 8, 64, 1024, 32768, 1146419, 8035168, 3434595, 29186, 1
Offset: 0
Examples
Array begins: ============================================================= n\k | 0 1 2 3 4 5 6 ----|------------------------------------------------------- 0 | 1 1 1 1 1 1 1 ... 1 | 1 2 2 2 2 2 2 ... 2 | 1 5 8 8 8 8 8 ... 3 | 1 14 45 64 64 64 64 ... 4 | 1 43 315 809 1024 1024 1024 ... 5 | 1 142 2634 13846 28217 32768 32768 ... 6 | 1 499 25518 301262 1146419 1914733 2097152 ... 7 | 1 1850 280257 8035168 62951431 178499118 254409765 ... ...
Crossrefs
Formula
T(n,k) = 2^(n*(n+1)/2) = A006125(n+1) for k >= n.