A099912 Number of closed walks on the Herschel graph.

1, 4, 32, 328, 3560, 39064, 429512, 4724248, 51965960, 571624024, 6287861192, 69166466968, 760831124360, 8369142343384, 92060565728072, 1012666222910488, 11139328451818760, 122532612969613144, 1347858742664958152

Offset

0,2

Comments

Counts closed walks of length 2n at any node of degree 4 on the Herschel graph. With interpolated zeros, counts closed walks of length n. The g.f. is then (1-9x^2+2x^4)/((1-2x^2)(1-11x^2))=(1-14x^2+53x^4-64x^6+12x^8)/((1-2x^2)^2(1-3x^2)(1-11x^2)). Binomial transform of A099913.

Links

Table of n, a(n) for n=0..18.

Eric Weisstein's World of Mathematics, Herschel Graph

Formula

G.f. : (1-9x+2x^2)/((1-2x)(1-11x)); a(n)=0^n/11+811^(n-1)/3+2^(n+1)/3.

Crossrefs

Sequence in context: A371675 A061631 A291342 * A362676 A272823 A371655

Adjacent sequences: A099909 A099910 A099911 * A099913 A099914 A099915

Keyword

easy,nonn

Author

Paul Barry, Oct 30 2004

Status

approved