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.
Original entry on oeis.org
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
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;
...
-
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)
A247596
Number of nonisomorphic binary n X n matrices with three 1's per column under row and column permutations.
Original entry on oeis.org
1, 5, 35, 410, 6178, 122038, 2921607, 81609320, 2588949454, 91699869557, 3582942335285, 153048366545566, 7096576775166579, 355120233277118103, 19084972486216897560, 1096965038775477639368, 67192642484367187943761, 4372413334294007638726854
Offset: 3
-
seq(matrix_marks(n,3), n=3..15); # Using the uploaded program to A247417
-
\\ See A304942 for Blocks
a(n) = Blocks(n, n, 3); \\ Andrew Howroyd, May 23 2018
A247597
Number of nonisomorphic binary n X n matrices with four 1's per column under row and column permutations.
Original entry on oeis.org
1, 7, 132, 6178, 594203, 85820809, 16341829155, 3875736708590, 1112175913348040, 378860991866916370, 151006214911844288232, 69600017255860985666964, 36729204987785981237238642, 22003003913198378660826731007, 14851323097928973689736994569534
Offset: 4
-
seq(matrix_marks(n,4), n=3..15); # Using the uploaded program to A247417
-
\\ See A304942 for Blocks
a(n) = Blocks(n, n, 4); \\ Andrew Howroyd, May 24 2018
A247598
Number of nonisomorphic binary n X n matrices with five 1's per column under row and column permutations.
Original entry on oeis.org
1, 11, 471, 122038, 85820809, 96018336018, 146662126879117, 291352421255114277, 734102568216405642199, 2304488853198195872625924, 8882860158091727486388086786, 41519759838668575020971562079517, 232748666229847254694256869145439898, 1549417862125158239133077344950011140191
Offset: 5
-
seq(matrix_marks(n,5), n=3..15); # Using the uploaded program to A247417
-
\\ See A304942 for Blocks
a(n) = Blocks(n, n, 5); \\ Andrew Howroyd, May 24 2018
Showing 1-4 of 4 results.