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