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A221042 The Wiener index of the Bethe cactus lattice graph D_n defined pictorially in the Hosoya - Balasubramanian reference. 1
8, 212, 3632, 50504, 624632, 7190492, 78973664, 839594768, 8717571176, 88915009892, 894366753296, 8896551656792, 87694439633240, 857879937077612, 8338591552929728, 80606380453484576, 775488956137204424, 7429684469671844852, 70919715248730034160, 674750433200813750120 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

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

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

LINKS

Table of n, a(n) for n=1..20.

FORMULA

a(n) = (1/2)+3^n*(3*n+4)+3^(2*n)*(3*n-9/2).

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

MAPLE

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);

CROSSREFS

Cf. A221043.

Sequence in context: A197767 A024288 A081794 * A247032 A027646 A224096

Adjacent sequences:  A221039 A221040 A221041 * A221043 A221044 A221045

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Dec 30 2012

STATUS

approved

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Last modified November 29 21:32 EST 2021. Contains 349416 sequences. (Running on oeis4.)