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

8, 212, 3632, 50504, 624632, 7190492, 78973664, 839594768, 8717571176, 88915009892, 894366753296, 8896551656792, 87694439633240, 857879937077612, 8338591552929728, 80606380453484576, 775488956137204424, 7429684469671844852, 70919715248730034160, 674750433200813750120

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 * A358211 A247032 A027646

Adjacent sequences: A221039 A221040 A221041 * A221043 A221044 A221045

Keyword

nonn,easy

Author

Emeric Deutsch, Dec 30 2012

Status

approved