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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.
2
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.
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. 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
KEYWORD
nonn,tabl,more
AUTHOR
STATUS
approved