A221045 The hyper-Wiener index of the Bethe cactus lattice graph C_n defined pictorially in the Hosoya - Balasubramanian reference.

10, 792, 22002, 419568, 6592794, 92192136, 1193312130, 14623811808, 172078919466, 1962477443832, 21832497397266, 238041018275280, 2552456907780666, 26988260347784040, 281967905150124450, 2915727266397879744, 29880877053048885834, 303816557606831292120

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..18.

Formula

a(n) = (3/2)-3^(n-1)*53+3^(2*n-2)*(64*n^2-148*n)+(97/6)*3^(2*n).

G.f.: 2*x*(5+241*x+495*x^2+27*x^3)/((1-x)*(1-3*x)*(1-9*x)^3). - Bruno Berselli, Dec 30 2012

Maple

a := proc (n) options operator, arrow: 3/2-53*3^(n-1)+3^(2*n-2)*(64*n^2-148*n)+(97/6)*3^(2*n) end proc: seq(a(n), n = 1 .. 18);

Crossrefs

Cf. A221044.

Sequence in context: A159709 A222689 A242373 * A015057 A302133 A322918

Adjacent sequences: A221042 A221043 A221044 * A221046 A221047 A221048

Keyword

nonn,easy

Author

Emeric Deutsch, Dec 30 2012

Extensions

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

Status

approved