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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.

%I A350364 #10 Dec 29 2021 11:18:26
%S A350364 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,
%T A350364 66,14,0,0,1,7,36,118,212,174,20,0,0,1,8,49,208,560,758,462,20,0,0,1,
%U A350364 9,64,334,1206,2620,2722,1178,22,0,0
%N 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.
%C A350364 T(n,2) = 0 for n >= 15.
%C A350364 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.)
%H A350364 Pontus von Brömssen, <a href="/A350364/b350364.txt">Antidiagonals n = 0..14, flattened</a>
%e A350364 Array begins:
%e A350364   n\k|  0  1  2    3     4      5       6       7
%e A350364   ---+-------------------------------------------
%e A350364    0 |  1  1  1    1     1      1       1       1
%e A350364    1 |  0  1  2    3     4      5       6       7
%e A350364    2 |  0  1  4    9    16     25      36      49
%e A350364    3 |  0  0  6   24    58    118     208     334
%e A350364    4 |  0  0 10   66   212    560    1206    2282
%e A350364    5 |  0  0 14  174   758   2620    6932   15506
%e A350364    6 |  0  0 20  462  2722  12277   39871  105405
%e A350364    7 |  0  0 20 1178  9628  57084  228451  714878
%e A350364    8 |  0  0 22 3036 34132 265659 1309476 4849364
%Y A350364 Cf. A350330, A350365.
%Y A350364 Cf. A000012 (row n = 0), A001477 (row n = 1), A000290 (row n = 2), A000007 (column k = 0), A130716 (column k = 1).
%K A350364 nonn,tabl
%O A350364 0,8
%A A350364 _Pontus von Brömssen_, Dec 27 2021