A304942 Triangle read by rows: T(n,k) is the number of nonisomorphic binary n X n matrices with k 1's per column under row and column permutations.
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 5, 11, 5, 1, 1, 7, 35, 35, 7, 1, 1, 11, 132, 410, 132, 11, 1, 1, 15, 471, 6178, 6178, 471, 15, 1, 1, 22, 1806, 122038, 594203, 122038, 1806, 22, 1, 1, 30, 7042, 2921607, 85820809, 85820809, 2921607, 7042, 30, 1
Offset: 0
Examples
Triangle begins (n >=0, k >= 0): 1; 1, 1; 1, 2, 1; 1, 3, 3, 1; 1, 5, 11, 5, 1; 1, 7, 35, 35, 7, 1; 1, 11, 132, 410, 132, 11, 1; 1, 15, 471, 6178, 6178, 471, 15, 1; 1, 22, 1806, 122038, 594203, 122038, 1806, 22, 1; ...
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..527
- StackExchange, How many arrays with crossed cells, order of rows/columns irrelevant, Dec 13 2013
Programs
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PARI
permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m} K(q,t,k)={polcoeff(prod(j=1, #q, my(g=gcd(t, q[j])); (1 + x^(q[j]/g) + O(x*x^k))^g), k)} Blocks(n,m,k)={my(s=0); forpart(q=m, s+=permcount(q)*polcoeff(exp(sum(t=1, n, K(q,t,k)/t*x^t) + O(x*x^n)), n)); s/m!} for(n=0, 10, for(k=0, n, print1(Blocks(n,n,k), ", ")); print)