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A263201
Number of perfect matchings on a Möbius strip of width 4 and length n.
1
11, 37, 71, 252, 539, 1813, 4271, 13519, 34276, 103803, 276119, 813417, 2226851, 6455052, 17965151, 51604017, 144948419, 414258603, 1169523076, 3333192319, 9436433171, 26853404413, 76139155439, 216490730652, 614339685971, 1745997031837, 4956888901511
OFFSET
2,1
COMMENTS
This sequence obeys the same recurrence relation as A252054.
LINKS
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
Sequence in context: A031381 A358079 A160023 * A337832 A188135 A188382
KEYWORD
nonn
AUTHOR
Sergey Perepechko, Oct 12 2015
STATUS
approved