[go: up one dir, main page]

login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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.
6
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
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
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, May 06 2021
STATUS
approved