A353436 Array read by descending antidiagonals: T(n,m) is the number of sequences of length n >= 0 with elements in 1..m-1 such that the determinant of the Hankel matrix of any odd number of consecutive terms is not divisible by m >= 1.

1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 4, 0, 0, 1, 4, 9, 4, 0, 0, 1, 5, 16, 22, 4, 0, 0, 1, 6, 25, 48, 56, 0, 0, 0, 1, 7, 36, 104, 144, 114, 0, 0, 0, 1, 8, 49, 180, 444, 320, 240, 0, 0, 0, 1, 9, 64, 298, 900, 1566, 720, 376, 0, 0, 0, 1, 10, 81, 468, 1828, 3744, 5576, 1312, 584, 0, 0, 0

Offset: 0

Author

Pontus von Brömssen, Apr 21 2022

Keywords

• nonn
• tabl

Examples

			Array begins:
  n\m| 1  2  3   4    5      6       7        8         9
  ---+---------------------------------------------------
   0 | 1  1  1   1    1      1       1        1         1
   1 | 0  1  2   3    4      5       6        7         8
   2 | 0  1  4   9   16     25      36       49        64
   3 | 0  0  4  22   48    104     180      298       468
   4 | 0  0  4  56  144    444     900     1828      3444
   5 | 0  0  0 114  320   1566    3744     9812     23208
   6 | 0  0  0 240  720   5576   15552    52784    157104
   7 | 0  0  0 376 1312  16544   54216   249424    968616
   8 | 0  0  0 584 2400  49900  189468  1191264   5991624
   9 | 0  0  0 724 3232 124052  550728  4955824  33844176
  10 | 0  0  0 920 4560 314932 1604088 20623232 191898648
		

Crossrefs

Cf. A353434, A353435.

Rows: A000012 (n=0), A001477 (n=1), A000290 (n=2).

Columns: A000007 (m=1), A130716 (m=2).

Formula

T(n,m) = A353435(n,m) if m is prime.

T(n,1) = 0 if n >= 1.

T(n,2) = 0 if n >= 3.

T(n,3) = 0 if n >= 5.

T(n,4) = 0 if n >= 25.

T(n,5) = 0 if n >= 23.