

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
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OFFSET

1,1


REFERENCES

K. Balasubramanian, Recent developments in treepruning methods and polynomials for cactus graphs and trees, J. Math. Chemistry, 4 (1990) 89102.
H. Hosoya, K. Balasubramanian, Exact dimer statistics and characteristic polynomials of cacti lattices, Theor. Chim. Acta 76 (1989) 315329.


LINKS

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


FORMULA

a(n) = (1/2)+3^n*(3*n+4)+3^(2*n)*(3*n9/2).
G.f.: 4*x*(2+3*x+27*x^2)/((1x)*(13*x)^2*(19*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*n9/2) 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



