A184265 Number of distinct n X 3 toroidal binary arrays.

4, 14, 64, 352, 2192, 14624, 99880, 699252, 4971184, 35792568, 260301176, 1908882592, 14096303344, 104715443852, 781874941184, 5864062367252, 44152937528384, 333599974922264, 2528336632928152, 19215358428046176, 146402730743992960, 1117984489446008100

Offset: 1

Author

R. H. Hardin, Jan 10 2011

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..1000
• S. N. Ethier, Counting toroidal binary arrays, arXiv preprint arXiv:1301.2352, 2013 and J. Int. Seq. 16 (2013) #13.4.7 .

Crossrefs

Column 3 of A184271.

Programs

Maple

with(numtheory):
a:= n-> add(add(phi(c)*phi(d) *2^(3*n/ilcm(c, d)),
        d=divisors(n)), c=[1, 3])/(3*n):
seq(a(n), n=1..30);  # Alois P. Heinz, Aug 25 2012

Formula

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

Extensions

More terms from Alois P. Heinz, Aug 25 2012