A350364 Array read by antidiagonals: T(n,k) is the number of sequences of length n with terms in 1..k such that all Hankel matrices of an odd number of consecutive terms are invertible, n, k >= 0.

1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 4, 0, 0, 1, 4, 9, 6, 0, 0, 1, 5, 16, 24, 10, 0, 0, 1, 6, 25, 58, 66, 14, 0, 0, 1, 7, 36, 118, 212, 174, 20, 0, 0, 1, 8, 49, 208, 560, 758, 462, 20, 0, 0, 1, 9, 64, 334, 1206, 2620, 2722, 1178, 22, 0, 0

Offset: 0

Author

Pontus von Brömssen, Dec 27 2021

Keywords

• nonn
• tabl

Comments

T(n,2) = 0 for n >= 15.

For a fixed k, what can be said about T(n,k) as n grows? (For k <= 2, T(n,k) = 0 for large n.)

Examples

			Array begins:
  n\k|  0  1  2    3     4      5       6       7
  ---+-------------------------------------------
   0 |  1  1  1    1     1      1       1       1
   1 |  0  1  2    3     4      5       6       7
   2 |  0  1  4    9    16     25      36      49
   3 |  0  0  6   24    58    118     208     334
   4 |  0  0 10   66   212    560    1206    2282
   5 |  0  0 14  174   758   2620    6932   15506
   6 |  0  0 20  462  2722  12277   39871  105405
   7 |  0  0 20 1178  9628  57084  228451  714878
   8 |  0  0 22 3036 34132 265659 1309476 4849364
		

Links

• Pontus von Brömssen, Antidiagonals n = 0..14, flattened

Crossrefs

Cf. A350330, A350365.

Cf. A000012 (row n = 0), A001477 (row n = 1), A000290 (row n = 2), A000007 (column k = 0), A130716 (column k = 1).