A184270 Number of distinct n X 8 toroidal binary arrays.

36, 4150, 699252, 134223976, 27487816992, 5864063066500, 1286742755471400, 288230376353050816, 65588423374144427520, 15111572745224096425720, 3516875111606393874082104, 825293359523595646117352176, 195023169265881489687952047216

Offset: 1

Author

R. H. Hardin, Jan 10 2011

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..410
• S. N. Ethier, Counting toroidal binary arrays, arXiv preprint arXiv:1301.2352, 2013 and J. Int. Seq. 16 (2013) #13.4.7.

Crossrefs

Column 8 of A184271.

Programs

Maple

with(numtheory):
a:= n-> add(add(phi(c)*phi(d) *2^(8*n/ilcm(c, d)),
        d=divisors(n)), c=[1,2,4,8])/(8*n):
seq(a(n), n=1..20);  # Alois P. Heinz, Aug 25 2012

Formula

a(n) ~ 2^(8*n-3) / n. - Vaclav Kotesovec, Sep 04 2014

Extensions

More terms from Alois P. Heinz, Aug 25 2012