A221044 The Wiener index of the Bethe cactus lattice graph C_n defined pictorially in the Hosoya - Balasubramanian reference.

8, 352, 6568, 92608, 1143880, 13115680, 143509480, 1521045376, 15755283592, 160392633568, 1610896046632, 16004345360704, 157595696236744, 1540370736608416, 14961422399467624, 144535575132212992, 1389765142844188936, 13308390999949846624, 126980061472109030056, 1207661435632198248640

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