cp's OEIS Frontend

A350365 Array read by antidiagonals: T(n,k) is the number of sequences of length 2*n+1 with terms in 0..k such that the Hankel matrix of the sequence is singular, but the Hankel matrix of any proper subsequence with an odd number of consecutive terms is invertible, n, k >= 0.

%I A350365 #5 Dec 27 2021 11:05:34
%S A350365 1,1,0,1,1,0,1,2,0,0,1,3,2,0,0,1,6,6,10,0,0,1,7,16,52,0,0,0,1,8,36,
%T A350365 148,116,8,0,0,1,9,58,448,644,528,12,0,0,1,12,82,885,2932,4032,1326,0,
%U A350365 0,0
%N A350365 Array read by antidiagonals: T(n,k) is the number of sequences of length 2*n+1 with terms in 0..k such that the Hankel matrix of the sequence is singular, but the Hankel matrix of any proper subsequence with an odd number of consecutive terms is invertible, n, k >= 0.
%C A350365 T(n,2) = 0 for n = 4 and for n >= 7.
%e A350365 Array begins:
%e A350365   n\k|  0  1  2   3   4    5
%e A350365   ---+----------------------
%e A350365    0 |  1  1  1   1   1    1
%e A350365    1 |  0  1  2   3   6    7
%e A350365    2 |  0  0  2   6  16   36
%e A350365    3 |  0  0 10  52 148  448
%e A350365    4 |  0  0  0 116 644 2932
%e A350365 For n = 2 and k = 4, the following T(2,4) = 16 sequences are counted:
%e A350365   (1, 1, 2, 2, 4),
%e A350365   (1, 2, 1, 2, 1),
%e A350365   (1, 2, 2, 4, 4),
%e A350365   (1, 3, 1, 3, 1),
%e A350365   (1, 4, 1, 4, 1),
%e A350365   (2, 1, 2, 1, 2),
%e A350365   (2, 3, 2, 3, 2),
%e A350365   (2, 4, 2, 4, 2),
%e A350365   (3, 1, 3, 1, 3),
%e A350365   (3, 2, 3, 2, 3),
%e A350365   (3, 4, 3, 4, 3),
%e A350365   (4, 1, 4, 1, 4),
%e A350365   (4, 2, 2, 1, 1),
%e A350365   (4, 2, 4, 2, 4),
%e A350365   (4, 3, 4, 3, 4),
%e A350365   (4, 4, 2, 2, 1).
%Y A350365 Cf. A350330, A350364.
%Y A350365 Cf. A000012 (row n = 0), A132188 (row n = 1), A000007 (column k = 0), A019590 (column k = 1).
%K A350365 nonn,tabl,more
%O A350365 0,8
%A A350365 _Pontus von Brömssen_, Dec 27 2021