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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.
5
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
0,8
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.)
LINKS
EXAMPLE
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
CROSSREFS
Cf. A000012 (row n = 0), A001477 (row n = 1), A000290 (row n = 2), A000007 (column k = 0), A130716 (column k = 1).
Sequence in context: A261835 A353436 A286932 * A358575 A259475 A361952
KEYWORD
nonn,tabl
AUTHOR
STATUS
approved