cp's OEIS Frontend

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).

%I A235118 #17 Jul 26 2022 13:07:20
%S A235118 1,24,544,12416,283136,6457344,147267584,3358621696,76597559296,
%T A235118 1746902974464,39840303284224,908607856050176,20721936531193856,
%U A235118 472589633411088384,10777996606218174464,245805668662673145856,5605905156051426082816,127849665915439602991104
%N 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).
%C A235118 Row sums of A235117.
%H A235118 Colin Barker, <a href="/A235118/b235118.txt">Table of n, a(n) for n = 0..700</a>
%H A235118 E. Mandrescu, <a href="http://ajc.maths.uq.edu.au/pdf/53/ajc_v53_p077.pdf">Unimodality of some independence polynomials via their palindromicity</a>, Australasian J. of Combinatorics, 53, 2012, 77-82.
%H A235118 D. Stevanovic, <a href="http://www.pmf.ni.ac.rs/pmf/licne_prezentacije/101/radovi/GTN%20-%20Palindromic%20Independence%20Polynomial/GTN.34(1998).31-36.Acro6.pdf">Graphs with palindromic independence polynomial</a>, Graph Theory Notes of New  York, 34, 1998, 31-36.
%H A235118 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20,64).
%F A235118 a(0)=1, a(1)=24, a(n) = 20*a(n-1) + 64*a(n-2) for n>=2.
%F A235118 G.f.: (1 + 4*x)/(1 - 20*x - 64*x^2).
%F A235118 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
%F A235118 a(n) = 4^n*A126501(n). - _R. J. Mathar_, Jul 26 2022
%p A235118 G := (1+4*x)/(1-20*x-64*x^2): Gser := series(G, x = 0, 22): seq(coeff(Gser, x, j), j = 0 .. 20);
%o A235118 (PARI) Vec((1 + 4*x) / (1 - 20*x - 64*x^2) + O(x^30)) \\ _Colin Barker_, Jul 31 2017
%Y A235118 Cf. A235117.
%K A235118 nonn,easy
%O A235118 0,2
%A A235118 _Emeric Deutsch_, Jan 14 2014