A221043 The hyper-Wiener index of the Bethe cactus lattice graph D_n defined pictorially in the Hosoya - Balasubramanian reference.

10, 457, 11788, 223306, 3527782, 49658659, 646456696, 7958918644, 94000489378, 1075247030365, 11991524116804, 131012134626814, 1407240945512638, 14901372361780855, 155885329216404592, 1613748977026119016, 16554187553043529402, 168462466522953130609

Offset

1,1

Links

Table of n, a(n) for n=1..18.

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

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

Index entries for linear recurrences with constant coefficients, signature (37,-549,4185,-17523,40095,-45927,19683).

Formula

a(n) = -(7/8)+3^n*(2*n^2-(9/4)*n-10)+3^(2*n)*(4*n^2-(41/4)*n+(87/8)).

G.f.: x*(243*x^4+3807*x^3-369*x^2-87*x-10) / ((x-1)*(3*x-1)^3*(9*x-1)^3). [Colin Barker, Jan 01 2013]

Maple

a := proc (n) options operator, arrow: -7/8+3^n*(2*n^2-(9/4)*n-10)+3^(2*n)*(4*n^2-(41/4)*n+87/8) end proc: seq(a(n), n = 1 .. 18);

Crossrefs

Cf. A221042.

Sequence in context: A304289 A217523 A232773 * A337757 A288548 A289030

Adjacent sequences: A221040 A221041 A221042 * A221044 A221045 A221046

Keyword

nonn,easy

Author

Emeric Deutsch, Dec 30 2012

Extensions

Offset changed from 0 to 1 by Bruno Berselli, Dec 30 2012

Status

approved