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A221046 The Wiener index of the Bethe cactus lattice graph E_n defined pictorially in the Hosoya - Balasubramanian reference. 1
4, 184, 3496, 49936, 622444, 7182472, 78945232, 839496352, 8717236564, 88913887960, 894363033208, 8896539433648, 87694399775164, 857879807937448, 8338591136811424, 80606379119036224, 775488951875579044, 7429684456112127736, 70919715205726359880, 674750433064829158480 (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) = -(1/2)+3^n*(n+5)+3^(2*n)*(3*n-(9/2)).

G.f.: 4*x*(1+21*x-54*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*(n+5)+3^(2*n)*(3*n-9/2) end proc: seq(a(n), n = 1 .. 20);

CROSSREFS

Cf. A221047.

Sequence in context: A172018 A295285 A322915 * A024266 A174772 A146549

Adjacent sequences:  A221043 A221044 A221045 * A221047 A221048 A221049

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Dec 30 2012

STATUS

approved

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Last modified May 22 11:15 EDT 2022. Contains 353949 sequences. (Running on oeis4.)