A006239 Row 3 of array in A212801.

1, 13, 108, 793, 5611, 39312, 274933, 1923025, 13455396, 94169413, 659134543, 4613813568, 32296413241, 226074381637, 1582520088348, 11077641280225, 77543496352291, 542804506787088, 3799631657379853, 26597421924762793

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Number of Eulerian circuits in the Cartesian product of two directed cycles of lengths 3 and n. - Andrew Howroyd, Jan 14 2018

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• Germain Kreweras, Complexité et circuits Eulériens dans les sommes tensorielles de graphes, J. Combin. Theory, B 24 (1978), 202-212. See p. 211.
• Eric Weisstein's World of Mathematics, Checkers.

Crossrefs

Cf. A212801.

Programs

Mathematica

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}];
a[n_] := T[3, n] // Round;
Array[a, 20] (* Jean-François Alcover, Jul 04 2018 *)

Formula

Empirical g.f.: x*(1-7*x^2)/((1-x)*(1-7*x)*(1-5*x+7*x^2)). - Bruno Berselli, May 31 2012

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

Extensions

Revised by N. J. A. Sloane, May 27 2012