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A221044 The Wiener index of the Bethe cactus lattice graph C_n defined pictorially in the Hosoya - Balasubramanian reference. 1
8, 352, 6568, 92608, 1143880, 13115680, 143509480, 1521045376, 15755283592, 160392633568, 1610896046632, 16004345360704, 157595696236744, 1540370736608416, 14961422399467624, 144535575132212992, 1389765142844188936, 13308390999949846624, 126980061472109030056, 1207661435632198248640 (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) = -2+3^(n-1)*28+3^(2*n-1)*(16*n-22).

G.f.: 8*x*(1+22*x+9*x^2)/((1-x)*(1-3*x)*(1-9*x)^2). - Bruno Berselli, Dec 30 2012

MAPLE

a := proc (n) options operator, arrow: -2+28*3^(n-1)+3^(2*n-1)*(16*n-22) end proc: seq(a(n), n = 1 .. 20);

CROSSREFS

Cf. A221045.

Sequence in context: A079485 A193504 A158363 * A221163 A000436 A015507

Adjacent sequences:  A221041 A221042 A221043 * A221045 A221046 A221047

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Dec 30 2012

STATUS

approved

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Last modified March 23 16:52 EDT 2019. Contains 321432 sequences. (Running on oeis4.)