OFFSET
2,1
COMMENTS
This sequence obeys the same recurrence relation as A252054.
LINKS
Colin Barker, Table of n, a(n) for n = 2..1000
W. T. Lu and F. Y. Wu, Close-packed dimers on nonorientable surfaces, Physics Letters A, 293(2002), 235-246.
S. N. Perepechko, Recurrence relations for the number of perfect matchings on the Mobius strips (in Russian), Proc. of XIX international conference on computational mechanics and modern applied software systems (CMMASS'2015), Alushta, Crimea, 2015, 98-100.
Sergey Perepechko, Graph view
G. Tesler, Matchings in graphs on non-orientable surfaces, Journal of Combinatorial Theory B, 78(2000), 198-231.
Index entries for linear recurrences with constant coefficients, signature (1,13,-7,-61,12,128,0,-128,-12,61,7,-13,-1,1).
FORMULA
G.f.: z^2*(11 + 26*z - 109*z^2 - 223*z^3 + 294*z^4 + 620*z^5 - 306*z^6 -764*z^7 + 100*z^8 + 414*z^9 + 5*z^10 - 92*z^11 - 3*z^12 + 7*z^13)/((1 - z)*(1 + z)*(1 + z - 3*z^2 - z^3 + z^4)*(1 - z - 3*z^2 + z^3 + z^4)*(1 - z - 5*z^2 - z^3 + z^4)).
MATHEMATICA
CoefficientList[Series[(11 + 26 x - 109 x^2 - 223 x^3 + 294 x^4 + 620 x^5 - 306 x^6 - 764 x^7 + 100 x^8 + 414 x^9 + 5 x^10 - 92 x^11 - 3 x^12 + 7 x^13)/((1 - x) (1 + x) (1 + x - 3 x^2 - x^3 + x^4) (1 - x - 3 x^2 + x^3 + x^4) (1 - x - 5 x^2 - x^3 + x^4)), {x, 0, 33}], x] (* Vincenzo Librandi, Oct 12 2015 *)
PROG
(PARI) Vec(z^2*(11 + 26*z - 109*z^2 - 223*z^3 + 294*z^4 + 620*z^5 - 306*z^6 -764*z^7 + 100*z^8 + 414*z^9 + 5*z^10 - 92*z^11 - 3*z^12 + 7*z^13)/((1 - z)*(1 + z)*(1 + z - 3*z^2 - z^3 + z^4)*(1 - z - 3*z^2 + z^3 + z^4)*(1 - z - 5*z^2 - z^3 + z^4)) + O(z^50)) \\ Altug Alkan, Oct 12 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Sergey Perepechko, Oct 12 2015
STATUS
approved