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 A221042 The Wiener index of the Bethe cactus lattice graph D_n defined pictorially in the Hosoya - Balasubramanian reference. 1

%I

%S 8,212,3632,50504,624632,7190492,78973664,839594768,8717571176,

%T 88915009892,894366753296,8896551656792,87694439633240,

%U 857879937077612,8338591552929728,80606380453484576,775488956137204424,7429684469671844852,70919715248730034160,674750433200813750120

%N The Wiener index of the Bethe cactus lattice graph D_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) = (1/2)+3^n*(3*n+4)+3^(2*n)*(3*n-9/2).

%F G.f.: 4*x*(2+3*x+27*x^2)/((1-x)*(1-3*x)^2*(1-9*x)^2). - _Bruno Berselli_, Dec 30 2012

%p a := proc (n) options operator, arrow: 1/2+3^n*(3*n+4)+3^(2*n)*(3*n-9/2) end proc: seq(a(n), n = 1 .. 20);

%Y Cf. A221043.

%K nonn,easy

%O 1,1

%A _Emeric Deutsch_, Dec 30 2012

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Last modified January 22 16:30 EST 2022. Contains 350484 sequences. (Running on oeis4.)