OFFSET
0,9
COMMENTS
T(n,k) is also the number of equivalence classes of n X k binary matrices with an even number of 1's in each column under permutation of rows and columns.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1325
M. A. Harrison, On the number of classes of binary matrices, IEEE Trans. Computers, 22 (1973), 1048-1051.
M. A. Harrison, On the number of classes of binary matrices, IEEE Transactions on Computers, C-22.12 (1973), 1048-1052. (Annotated scanned copy)
EXAMPLE
Array begins:
======================================================
n/k| 0 1 2 3 4 5 6 7 8 ...
---+--------------------------------------------------
0 | 1 1 1 1 1 1 1 1 1 ...
1 | 1 1 1 1 1 1 1 1 1 ...
2 | 1 2 3 4 5 6 7 8 9 ...
3 | 1 2 4 7 11 16 23 31 41 ...
4 | 1 3 8 19 41 81 153 273 468 ...
5 | 1 3 10 32 101 299 849 2290 5901 ...
6 | 1 4 16 68 301 1358 6128 27008 114763 ...
7 | 1 4 20 114 757 5567 43534 343656 2645494 ...
8 | 1 5 29 210 1981 23350 319119 4633380 67013431 ...
...
PROG
(PARI) \\ Compare A028657.
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)={sum(j=1, #q, gcd(t, q[j]))}
T(n, k)={if(n==0, 1, my(s=0); forpart(q=n, my(e=1<<valuation(Vec(q), 2)); s+=permcount(q)*polcoef(exp(sum(t=1, k, 2^(K(q, t)-(t%e==0))/t*x^t) + O(x*x^k)), k)); s/n!)}
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, May 28 2023
STATUS
approved