A006239 Row 3 of array in A212801. (Formerly M4909)

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

Offset

1,2

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.

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

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 *)

Crossrefs

Cf. A212801.

Sequence in context: A038384 A038385 A084901 * A271560 A142040 A002648

Adjacent sequences: A006236 A006237 A006238 * A006240 A006241 A006242

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

Status

approved