A343874 Array read by antidiagonals: T(n,k) is the number of n X n nonnegative integer matrices with sum of elements equal to k, up to rotational symmetry.

1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 3, 3, 1, 0, 1, 5, 13, 4, 1, 0, 1, 10, 43, 36, 7, 1, 0, 1, 14, 129, 204, 85, 9, 1, 0, 1, 22, 327, 980, 735, 171, 13, 1, 0, 1, 30, 761, 3876, 5145, 2109, 313, 16, 1, 0, 1, 43, 1619, 13596, 29715, 20610, 5213, 528, 21, 1

Offset

0,13

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1325

Example

Array begins:
=====================================================
n\k | 0  1   2    3     4      5       6        7
----+------------------------------------------------
  0 | 1  0   0    0     0      0       0        0 ...
  1 | 1  1   1    1     1      1       1        1 ...
  2 | 1  1   3    5    10     14      22       30 ...
  3 | 1  3  13   43   129    327     761     1619 ...
  4 | 1  4  36  204   980   3876   13596    42636 ...
  5 | 1  7  85  735  5145  29715  148561   657511 ...
  6 | 1  9 171 2109 20610 164502 1124382  6744582 ...
  7 | 1 13 313 5213 67769 717509 6457529 50732669 ...
  ...

Prog

(PARI)
U(n, s)={(s(1)^(n^2) + s(1)^(n%2)*(2*s(4)^(n^2\4) + s(2)^(n^2\2)))/4}
T(n, k)={polcoef(U(n, i->1/(1-x^i) + O(x*x^k)), k)}

Crossrefs

Rows n=0..4 are A000007, A000012, A008610, A054771, A054773.

Columns k=0..1 are A000012, A004652.

Cf. A054772 (binary case), A318795, A343095, A343875.

Sequence in context: A290454 A281066 A343875 * A114795 A245669 A211648

Adjacent sequences: A343871 A343872 A343873 * A343875 A343876 A343877

Keyword

nonn,tabl

Author

Andrew Howroyd, May 06 2021

Status

approved