A103998 Number of dimer tilings of a 4 x 2n Moebius strip.

1, 11, 71, 539, 4271, 34276, 276119, 2226851, 17965151, 144948419, 1169523076, 9436433171, 76139155439, 614339685971, 4956888901511, 39995380044004, 322708555336511, 2603821045832171, 21009309912323639

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Index entries for linear recurrences with constant coefficients, signature (11, -25, 11, -1).

Formula

G.f.: (1-25x^2+22x^3-3x^4)/(1-11x+25x^2-11x^3+x^4).

a(0)=1, a(1)=11, a(2)=71, a(3)=539, a(4)=4271, a(n)=11*a(n-1)-25*a(n-2)+ 11*a(n-3)-a(n-4). - Harvey P. Dale, Jun 15 2011

Mathematica

Join[{1}, LinearRecurrence[{11, -25, 11, -1}, {11, 71, 539, 4271}, 40]] (* Harvey P. Dale, Jun 15 2011 *)
(* Alternative: *)
CoefficientList[ Series[ (1-25x^2+22x^3-3x^4)/ (1-11x+ 25x^2- 11x^3+x^4), {x, 0, 40}], x] (* Harvey P. Dale, Jun 15 2011 *)

Prog

(PARI) a(n)=if(n, ([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -1, 11, -25, 11]^(n-1)*[11; 71; 539; 4271])[1, 1], 1) \\ Charles R Greathouse IV, May 29 2026

Crossrefs

Cf. Second row of array A103997.

Sequence in context: A068847 A139185 A290123 * A160587 A338416 A034196

Adjacent sequences: A103995 A103996 A103997 * A103999 A104000 A104001

Keyword

nonn,easy,changed

Author

Ralf Stephan, Feb 26 2005

Status

approved