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.

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.

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.

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; [Conjectured by 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

njas