A212962 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; graph; refs; listen; history; text; internal format)

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