A263201 Number of perfect matchings on a Möbius strip of width 4 and length n.

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

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: A031381 A358079 A160023 * A337832 A188135 A188382

Adjacent sequences: A263198 A263199 A263200 * A263202 A263203 A263204

Keyword

nonn

Author

Sergey Perepechko, Oct 12 2015

Status

approved