A221046 The Wiener index of the Bethe cactus lattice graph E_n defined pictorially in the Hosoya - Balasubramanian reference.

4, 184, 3496, 49936, 622444, 7182472, 78945232, 839496352, 8717236564, 88913887960, 894363033208, 8896539433648, 87694399775164, 857879807937448, 8338591136811424, 80606379119036224, 775488951875579044, 7429684456112127736, 70919715205726359880, 674750433064829158480

Offset

1,1

Links

Ray Chandler, Table of n, a(n) for n = 1..1000

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 (25, -222, 846, -1377, 729).

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