cp's OEIS Frontend

A006239 Row 3 of array in A212801.

%I A006239 M4909 #32 Feb 16 2025 08:32:29
%S A006239 1,13,108,793,5611,39312,274933,1923025,13455396,94169413,659134543,
%T A006239 4613813568,32296413241,226074381637,1582520088348,11077641280225,
%U A006239 77543496352291,542804506787088,3799631657379853,26597421924762793
%N A006239 Row 3 of array in A212801.
%C A006239 Number of Eulerian circuits in the Cartesian product of two directed cycles of lengths 3 and n. - _Andrew Howroyd_, Jan 14 2018
%D A006239 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006239 Andrew Howroyd, <a href="/A006239/b006239.txt">Table of n, a(n) for n = 1..200</a>
%H A006239 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 A006239 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Checkers.html">Checkers</a>.
%F A006239 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 A006239 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 A006239 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 A006239 a[n_] := T[3, n] // Round;
%t A006239 Array[a, 20] (* _Jean-François Alcover_, Jul 04 2018 *)
%Y A006239 Cf. A212801.
%K A006239 nonn
%O A006239 1,2
%A A006239 _N. J. A. Sloane_
%E A006239 Revised by _N. J. A. Sloane_, May 27 2012