A263200 Number of perfect matchings on a Möbius strip of width 3 and length 2n.

28, 104, 388, 1448, 5404, 20168, 75268, 280904, 1048348, 3912488, 14601604, 54493928, 203374108, 759002504, 2832635908, 10571541128, 39453528604, 147242573288, 549516764548, 2050824484904, 7653781175068, 28564300215368, 106603419686404, 397849378530248

Offset

2,1

Comments

This sequence obeys the same recurrence relation as A001835.

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 (4,-1).

Formula

a(n) = Product_{k=1..n} (10 + 2*cos(Pi*(4*k-1)/n) - 12*cos(1/2*Pi*(4*k-1)/n)).

G.f.: 4*x^2*(7-2*x)/(1-4*x+x^2).

From Colin Barker, Oct 12 2015: (Start)

a(n) = 2*((2-sqrt(3))^n + (2+sqrt(3))^n).

a(n) = 4*a(n-1) - a(n-2). (End)

a(n) = 4*A001075(n) for n >= 2. - Philippe Deléham, Mar 03 2023

Mathematica

CoefficientList[Series[4 (7 - 2 x)/(1 - 4 x + x^2), {x, 0, 33}], x] (* Vincenzo Librandi, Oct 12 2015 *)

Prog

(PARI) Vec(4*x^2*(7-2*x)/(1-4*x+x^2) + O(x^30)) \\ Altug Alkan, Oct 12 2015
(Magma) I:=[28, 104]; [n le 2 select I[n] else 4*Self(n-1)-Self(n-2): n in [1..30]]; // Vincenzo Librandi, Oct 12 2015

Crossrefs

Cf. A001075, A001835, A020878.

Sequence in context: A255218 A168254 A219380 * A223443 A201469 A010016

Adjacent sequences: A263197 A263198 A263199 * A263201 A263202 A263203

Keyword

nonn,easy

Author

Sergey Perepechko, Oct 12 2015

Status

approved