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
Examples
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 ... ...
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..1325
Crossrefs
Programs
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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)}
Comments