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%I M4909 #31 Jul 04 2018 01:57:01
%S 1,13,108,793,5611,39312,274933,1923025,13455396,94169413,659134543,
%T 4613813568,32296413241,226074381637,1582520088348,11077641280225,
%U 77543496352291,542804506787088,3799631657379853,26597421924762793
%N Row 3 of array in A212801.
%C Number of Eulerian circuits in the Cartesian product of two directed cycles of lengths 3 and n. - _Andrew Howroyd_, Jan 14 2018
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Andrew Howroyd, <a href="/A006239/b006239.txt">Table of n, a(n) for n = 1..200</a>
%H Germain Kreweras, <a href="http://dx.doi.org/10.1016/0095-8956(78)90021-7">Complexité et circuits Eulériens dans les sommes tensorielles de graphes</a>, J. Combin. Theory, B 24 (1978), 202-212. See p. 211.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Checkers.html">Checkers</a>.
%F Empirical g.f.: x*(1-7*x^2)/((1-x)*(1-7*x)*(1-5*x+7*x^2)). - _Bruno Berselli_, May 31 2012
%F Empirical closed form: a(n) = (2^n*(1+7^n) -(5-i*sqrt(3))^n -(5+i*sqrt(3))^n) / (3*2^n), where i=sqrt(-1). - _Bruno Berselli_, May 31 2012
%t T[m_, n_] := Product[2 - Exp[2*I*h*Pi/m] - Exp[2*I*k*Pi/n], {h, 1, m - 1}, {k, 1, n - 1}];
%t a[n_] := T[3, n] // Round;
%t Array[a, 20] (* _Jean-François Alcover_, Jul 04 2018 *)
%Y Cf. A212801.
%K nonn
%O 1,2
%A _N. J. A. Sloane_
%E Revised by _N. J. A. Sloane_, May 27 2012
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