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A221044 The Wiener index of the Bethe cactus lattice graph C_n defined pictorially in the Hosoya - Balasubramanian reference. 1

%I

%S 8,352,6568,92608,1143880,13115680,143509480,1521045376,15755283592,

%T 160392633568,1610896046632,16004345360704,157595696236744,

%U 1540370736608416,14961422399467624,144535575132212992,1389765142844188936,13308390999949846624,126980061472109030056,1207661435632198248640

%N The Wiener index of the Bethe cactus lattice graph C_n defined pictorially in the Hosoya - Balasubramanian reference.

%D K. Balasubramanian, Recent developments in tree-pruning methods and polynomials for cactus graphs and trees, J. Math. Chemistry, 4 (1990) 89-102.

%D H. Hosoya, K. Balasubramanian, Exact dimer statistics and characteristic polynomials of cacti lattices, Theor. Chim. Acta 76 (1989) 315-329.

%F a(n) = -2+3^(n-1)*28+3^(2*n-1)*(16*n-22).

%F G.f.: 8*x*(1+22*x+9*x^2)/((1-x)*(1-3*x)*(1-9*x)^2). - _Bruno Berselli_, Dec 30 2012

%p a := proc (n) options operator, arrow: -2+28*3^(n-1)+3^(2*n-1)*(16*n-22) end proc: seq(a(n), n = 1 .. 20);

%Y Cf. A221045.

%K nonn,easy

%O 1,1

%A _Emeric Deutsch_, Dec 30 2012

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Last modified May 22 20:00 EDT 2022. Contains 353957 sequences. (Running on oeis4.)