A049293 Number of subgroups of index 3 in fundamental group of a closed surface of characteristic -n.

0, 0, 4, 34, 220, 1330, 7924, 47194, 281740, 1685410, 10095844, 60522154, 362968060, 2177301490, 13062263764, 78368897914, 470199235180, 2821152757570, 16926788191684, 101560343302474, 609360900699100

Offset

-2,3

References

V. A. Liskovets and A. Mednykh, Enumeration of subgroups in the fundamental groups of orientable circle bundles over surfaces, Commun. in Algebra, 28, No. 4 (2000), 1717-1738.

Links

Vincenzo Librandi, Table of n, a(n) for n = -2..1000

V. A. Liskovets and A. Mednykh, Number of non-orientable coverings of the Klein bottle, on ResearchGate.

A. D. Mednykh, On the number of subgroups in the fundamental group of a closed surface, Commun. in Algebra, 16, No 10 (1988), 2137-2148.

Index entries for linear recurrences with constant coefficients, signature (12,-47,72,-36).

Formula

a(n) = 6^(n+1)+3^(n+1)-3*2^(n+1)+1.

a(-2)=0, a(-1)=0, a(0)=4, a(1)=34, a(n)=12*a(n-1)-47*a(n-2)+72*a(n-3)- 36*a(n-4) [Harvey P. Dale, Mar 03 2012]

G.f.: 2*(2-7*x)/((1-x)*(1-2*x)*(1-3*x)*(1-6*x)). - Bruno Berselli, Mar 04 2012

Mathematica

Table[6^(n+1)+3^(n+1)-3*2^(n+1)+1, {n, -2, 20}] (* or *) LinearRecurrence[ {12, -47, 72, -36}, {0, 0, 4, 34}, 30] (* Harvey P. Dale, Mar 03 2012 *)

Prog

(PARI) a(n)=6^(n+1)+3^(n+1)-3<<(n+1)+1 \\ Charles R Greathouse IV, Mar 04, 2012

Crossrefs

Cf. A003319, A027837, A049290-A049295.

Sequence in context: A196908 A197075 A085695 * A198687 A116430 A216239

Adjacent sequences: A049290 A049291 A049292 * A049294 A049295 A049296

Keyword

nonn,easy,nice

Author

Valery A. Liskovets

Extensions

More terms from Karen Richardson (s1149414(AT)cedarville.edu)

Corrected by T. D. Noe, Nov 08 2006

Status

approved