1,8

(1+x)*(1+x^3)*(1+x^5)/((1-x^2)*(1-x^4)*(1-x^6)) is the Poincare series (or Molien series) for symmetric invariants in F_2(b_1, b_2, ... b_n) \otimes E(e_1, e_2, ... e_n) with b_i 2-dimensional, e_i one-dimensional and the permutation action of S_n, in the case n=3.

A. Adem and R. J. Milgram, Cohomology of Finite Groups, Springer-Verlag, 2nd. ed., 200

J. L. Gross and T. W. Tucker, Topological Graph Theory, Wiley, 1987; see I(n) p. 221.

J. L. Gross and J. Yellen, eds., Handbook of Graph Theory, CRC Press, 2004; p. 740.

G. Ringel and J. W. T. Youngs, Solution of the Heawood map-coloring problem, Proc. Nat. Acad. Sci. USA, 60 (1968), 438-445.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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

T. D. Noe, Table of n, a(n) for n=1..1000

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

Eric Weisstein's World of Mathematics, Graph Genus

Euler transform of length 10 sequence [1, 0, 1, 1, 1, 0, 0, 0, 0, -1]. - Michael Somos, Aug 24 2005

G.f.: x^5*(1+x^5)/((1-x)*(1-x^3)*(1-x^4)).

a(n) = Ceiling ( (n-3)*(n-4)/12 ) if n>=3.

a(1)=a(2)=a(3)=a(4)=0 because K_4 is planar. a(5)=a(6)=a(7)=1 because K_7 can be embedded on the torus of genus 1.

A000933:=-z**4*(1-z+z**2-z**3+z**4)/(z**2+z+1)/(1+z**2)/(z-1)**3; [S. Plouffe in his 1992 dissertation.]

(PARI) a(n)=if(n<3, 0, ceil((n-3)*(n-4)/12)) /* Michael Somos Aug 24 2005 */

Cf. A007997.

Sequence in context: A140642 A072666 A075471 this_sequence A036409 A005423 A067319

Adjacent sequences: A000930 A000931 A000932 this_sequence A000934 A000935 A000936

easy,nonn,nice

N. J. A. Sloane (njas(AT)research.att.com).