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

0,8

Comments

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

Links

Table of n, a(n) for n=0..54.

Example

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).

Sequence in context: A353434 A350529 A322279 * A331923 A342129 A292861

Adjacent sequences: A350362 A350363 A350364 * A350366 A350367 A350368

Keyword

nonn,tabl,more

Author

Pontus von Brömssen, Dec 27 2021

Status

approved