A063812 Growth series for fundamental group of orientable closed surface of genus 2.

1, 8, 56, 392, 2736, 19096, 133288, 930328, 6493536, 45323816, 316352792, 2208090536, 15412109328, 107573992120, 750848799112, 5240801312824, 36579932515008, 255321921769544, 1782105084785144, 12438800833105352

Offset

0,2

References

P. de la Harpe, Topics in Geometric Group Theory, Univ. Chicago Press, 2000, p. 160, Sigma(Gamma_2, S_2; z).

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,6,6,-1).

Formula

G.f.: (1 + x)^2*(1 + x^2) / (1 - 6*x - 6*x^2 - 6*x^3 + x^4).

a(n) = 6*a(n-1) + 6*a(n-2) + 6*a(n-3) - a(n-4) for n>4. - Colin Barker, Jun 13 2019

Prog

(PARI) Vec((1 + x)^2*(1 + x^2) / (1 - 6*x - 6*x^2 - 6*x^3 + x^4) + O(x^20)) \\ Colin Barker, Jun 13 2019

Crossrefs

Sequence in context: A010556 A010575 A162949 * A234274 A163347 A163924

Adjacent sequences: A063809 A063810 A063811 * A063813 A063814 A063815

Keyword

nonn,easy

Author

N. J. A. Sloane, Aug 21 2001

Status

approved