A235118 Number of independent vertex subsets of the graph obtained by attaching two pendant edges to each vertex of the ladder graph L_n (L_n is the 2 X n grid graph; see A235117).
1, 24, 544, 12416, 283136, 6457344, 147267584, 3358621696, 76597559296, 1746902974464, 39840303284224, 908607856050176, 20721936531193856, 472589633411088384, 10777996606218174464, 245805668662673145856, 5605905156051426082816, 127849665915439602991104
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..700
- E. Mandrescu, Unimodality of some independence polynomials via their palindromicity, Australasian J. of Combinatorics, 53, 2012, 77-82.
- D. Stevanovic, Graphs with palindromic independence polynomial, Graph Theory Notes of New York, 34, 1998, 31-36.
- Index entries for linear recurrences with constant coefficients, signature (20,64).
Crossrefs
Cf. A235117.
Programs
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Maple
G := (1+4*x)/(1-20*x-64*x^2): Gser := series(G, x = 0, 22): seq(coeff(Gser, x, j), j = 0 .. 20);
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PARI
Vec((1 + 4*x) / (1 - 20*x - 64*x^2) + O(x^30)) \\ Colin Barker, Jul 31 2017
Formula
a(0)=1, a(1)=24, a(n) = 20*a(n-1) + 64*a(n-2) for n>=2.
G.f.: (1 + 4*x)/(1 - 20*x - 64*x^2).
a(n) = (((-7+sqrt(41))*(-2*(-5+sqrt(41)))^n + (2*(5+sqrt(41)))^n*(7+sqrt(41))) / (2*sqrt(41))). - Colin Barker, Jul 31 2017
a(n) = 4^n*A126501(n). - R. J. Mathar, Jul 26 2022
Comments