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
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
More terms from Karen Richardson (s1149414(AT)cedarville.edu)
Corrected by T. D. Noe, Nov 08 2006
STATUS
approved