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%I #8 Dec 30 2012 17:00:54
%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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