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.

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, 148, 116, 8, 0, 0, 1, 9, 58, 448, 644, 528, 12, 0, 0, 1, 12, 82, 885, 2932, 4032, 1326, 0, 0, 0

Offset: 0

Author

Pontus von Brömssen, Dec 27 2021

Keywords

• nonn
• tabl
• more

Comments

T(n,2) = 0 for n = 4 and for n >= 7.

Examples

			Array begins:
  n\k|  0  1  2   3   4    5
  ---+----------------------
   0 |  1  1  1   1   1    1
   1 |  0  1  2   3   6    7
   2 |  0  0  2   6  16   36
   3 |  0  0 10  52 148  448
   4 |  0  0  0 116 644 2932
For n = 2 and k = 4, the following T(2,4) = 16 sequences are counted:
  (1, 1, 2, 2, 4),
  (1, 2, 1, 2, 1),
  (1, 2, 2, 4, 4),
  (1, 3, 1, 3, 1),
  (1, 4, 1, 4, 1),
  (2, 1, 2, 1, 2),
  (2, 3, 2, 3, 2),
  (2, 4, 2, 4, 2),
  (3, 1, 3, 1, 3),
  (3, 2, 3, 2, 3),
  (3, 4, 3, 4, 3),
  (4, 1, 4, 1, 4),
  (4, 2, 2, 1, 1),
  (4, 2, 4, 2, 4),
  (4, 3, 4, 3, 4),
  (4, 4, 2, 2, 1).
		

Crossrefs

Cf. A350330, A350364.

Cf. A000012 (row n = 0), A132188 (row n = 1), A000007 (column k = 0), A019590 (column k = 1).