A184264 Number of distinct n X 2 toroidal binary arrays.

3, 7, 14, 40, 108, 362, 1182, 4150, 14602, 52588, 190746, 699600, 2581428, 9588742, 35792568, 134223910, 505294128, 1908896442, 7233642930, 27487869472, 104715443852, 399822696082, 1529755490574, 5864063066500, 22517998808028, 86607689013412, 333599974893066

Offset: 1

Author

R. H. Hardin, Jan 10 2011

Keywords

• nonn

Links

• Alois P. Heinz, 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 2 of A184271.

Programs

Maple

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

Formula

a(n) ~ 2^(2*n-1) / n. - Vaclav Kotesovec, Sep 04 2014

Extensions

More terms from Alois P. Heinz, Aug 25 2012