A212962 Expansion of x*(3+x-x^3)/((1-3*x-x^2)*(1-x)*(1+x)).

0, 3, 10, 36, 118, 393, 1297, 4287, 14158, 46764, 154450, 510117, 1684801, 5564523, 18378370, 60699636, 200477278, 662131473, 2186871697, 7222746567, 23855111398, 78788080764, 260219353690, 859446141837, 2838557779201, 9375119479443

Offset

0,2

Comments

Counts configuration of dimers on lattice strips.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Yong Kong, Monomer-dimer model in two-dimensional rectangular lattices with fixed dimer density, arXiv:cond-mat/0610690, 2006, v_c(n).

Index entries for linear recurrences with constant coefficients, signature (3,2,-3,-1).

Formula

a(n+1) = 2*A006190(n)+3*A006190(n+1)-A000035(n).

Mathematica

CoefficientList[Series[x (3 + x - x^3)/((1 - 3*x - x^2)*(1-x)*(1+x)), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 23 2012 *)
LinearRecurrence[{3, 2, -3, -1}, {0, 3, 10, 36, 118}, 30] (* Harvey P. Dale, Sep 29 2023 *)

Prog

(Magma) I:=[0, 3, 10, 36, 118]; [n le 5 select I[n] else 3*Self(n-1)+2*Self(n-2)-3*Self(n-3)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 23 2012

Crossrefs

Sequence in context: A319733 A075316 A192142 * A246975 A047122 A047107

Adjacent sequences: A212959 A212960 A212961 * A212963 A212964 A212965

Keyword

nonn,easy

Author

R. J. Mathar, Jun 28 2012

Extensions

Offset changed from 1 to 0, added a(0)=0 by Vincenzo Librandi, Dec 23 2012

Status

approved