A184264 - OEIS

%I #23 Jan 20 2018 16:12:45

%S 3,7,14,40,108,362,1182,4150,14602,52588,190746,699600,2581428,

%T 9588742,35792568,134223910,505294128,1908896442,7233642930,

%U 27487869472,104715443852,399822696082,1529755490574,5864063066500,22517998808028,86607689013412,333599974893066

%N Number of distinct n X 2 toroidal binary arrays.

%H Alois P. Heinz, <a href="/A184264/b184264.txt">Table of n, a(n) for n = 1..1000</a>

%H S. N. Ethier, <a href="http://arxiv.org/abs/1301.2352">Counting toroidal binary arrays</a>, arXiv preprint arXiv:1301.2352, 2013 and <a href="https://cs.uwaterloo.ca/journals/JIS/VOL16/Ethier/ethier2.html">J. Int. Seq. 16 (2013) #13.4.7</a> .

%F a(n) ~ 2^(2*n-1) / n. - _Vaclav Kotesovec_, Sep 04 2014

%p with(numtheory):

%p a:= n-> add(add(phi(c)*phi(d) *2^(2*n/ilcm(c, d)),

%p         d=divisors(n)), c=[1,2])/(2*n):

%p seq(a(n), n=1..30);  # _Alois P. Heinz_, Aug 25 2012

%Y Column 2 of A184271.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 10 2011

%E More terms from _Alois P. Heinz_, Aug 25 2012