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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 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A020878, A263200. Sequence in context: A265767 A031381 A160023 * A188135 A188382 A090950 Adjacent sequences:  A263198 A263199 A263200 * A263202 A263203 A263204 KEYWORD nonn AUTHOR Sergey Perepechko, Oct 12 2015 STATUS approved

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Last modified August 14 13:36 EDT 2018. Contains 313751 sequences. (Running on oeis4.)