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Number of distinct n X 3 toroidal binary arrays.
2

%I #22 Jan 20 2018 16:13:21

%S 4,14,64,352,2192,14624,99880,699252,4971184,35792568,260301176,

%T 1908882592,14096303344,104715443852,781874941184,5864062367252,

%U 44152937528384,333599974922264,2528336632928152,19215358428046176,146402730743992960,1117984489446008100

%N Number of distinct n X 3 toroidal binary arrays.

%H Vaclav Kotesovec, <a href="/A184265/b184265.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) ~ 8^n / (3*n). - _Vaclav Kotesovec_, Sep 04 2014

%p with(numtheory):

%p a:= n-> add(add(phi(c)*phi(d) *2^(3*n/ilcm(c, d)),

%p d=divisors(n)), c=[1, 3])/(3*n):

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

%Y Column 3 of A184271.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 10 2011

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