A343875 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 rotations and reflections.

1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 3, 3, 1, 0, 1, 4, 11, 3, 1, 0, 1, 8, 31, 24, 6, 1, 0, 1, 10, 84, 113, 55, 6, 1, 0, 1, 16, 198, 528, 410, 99, 10, 1, 0, 1, 20, 440, 2003, 2710, 1091, 181, 10, 1, 0, 1, 29, 904, 6968, 15233, 10488, 2722, 288, 15, 1, 0, 1, 35, 1766, 21593, 75258, 82704, 34399, 5806, 461, 15, 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    4     8     10      16       20 ...
  3 | 1  3  11   31    84    198     440      904 ...
  4 | 1  3  24  113   528   2003    6968    21593 ...
  5 | 1  6  55  410  2710  15233   75258   331063 ...
  6 | 1  6  99 1091 10488  82704  563864  3376134 ...
  7 | 1 10 181 2722 34399 360676 3235551 25387944 ...
  ...

Prog

(PARI)
U(n, s) = {(s(1)^(n^2) + s(1)^(n%2)*(2*s(4)^(n^2\4) + s(2)^(n^2\2)) + 2*s(1)^n*s(2)^(n*(n-1)/2) + 2*(s(1)^(n%2)*s(2)^(n\2))^n )/8}
T(n, k)={polcoef(U(n, i->1/(1-x^i) + O(x*x^k)), k)}

Crossrefs

Rows n=0..3 are A000007, A000012, A005232, A054343.

Columns 0..1 are A000012, A008805(n-1).

Cf. A054252 (binary case), A318795, A343097, A343874.

Sequence in context: A229158 A290454 A281066 * A343874 A114795 A245669

Adjacent sequences: A343872 A343873 A343874 * A343876 A343877 A343878

Keyword

nonn,tabl

Author

Andrew Howroyd, May 06 2021

Status

approved