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

0,5

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

Example

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;
  ...

Prog

(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)

Crossrefs

Columns k=1..5 are A000041, A247417, A247596, A247597, A247598.

Cf. A305027.

Sequence in context: A183610 A261365 A261507 * A090011 A061554 A296373

Adjacent sequences: A304939 A304940 A304941 * A304943 A304944 A304945

Keyword

nonn,tabl

Author

Andrew Howroyd, May 23 2018

Status

approved