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A221046 The Wiener index of the Bethe cactus lattice graph E_n defined pictorially in the Hosoya - Balasubramanian reference. 1

%I

%S 4,184,3496,49936,622444,7182472,78945232,839496352,8717236564,

%T 88913887960,894363033208,8896539433648,87694399775164,

%U 857879807937448,8338591136811424,80606379119036224,775488951875579044,7429684456112127736,70919715205726359880,674750433064829158480

%N The Wiener index of the Bethe cactus lattice graph E_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*(n+5)+3^(2*n)*(3*n-(9/2)).

%F G.f.: 4*x*(1+21*x-54*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*(n+5)+3^(2*n)*(3*n-9/2) end proc: seq(a(n), n = 1 .. 20);

%Y Cf. A221047.

%K nonn,easy

%O 1,1

%A _Emeric Deutsch_, Dec 30 2012

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Last modified June 27 16:27 EDT 2022. Contains 354896 sequences. (Running on oeis4.)