A221015 The hyper-Wiener index of the dendrimer G_n , defined pictorially in the Ashrafi - Shabani - Diudea reference.

1932, 53181, 650751, 5617899, 40053075, 253523331, 1481003043, 8169745635, 43181452131, 220829474403, 1100143233123, 5365599704163, 25713603050595, 121424081661027, 566235515047011, 2612143455243363, 11937564067826787, 54106970144246883

Offset

1,1

Links

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

A. R. Ashrafi, H. Shabani, M. V. Diudea, Balaban index of dendrimers, MATCH, Commun. Math. Comput. Chem. 69, 2013, 151-158.

Formula

a(n) = 3171 + 2^(n-1)*(-810*n^2 +3240*n -35583) + 4^(n-1)*(11664*n^2 -38232*n+58482).

G.f.: 3*x*(644+5491*x-23296*x^2+676*x^3+38816*x^4+6208*x^5)/((1-x)*(1-2*x)^3*(1-4*x)^3). - Bruno Berselli, Dec 30 2012

Maple

a := proc (n) options operator, arrow: 3171+2^(n-1)*(-810*n^2+3240*n-35583)+4^(n-1)*(11664*n^2-38232*n+58482) end proc: seq(a(n), n = 1 .. 18);

Crossrefs

Cf. A221014.

Sequence in context: A283925 A166393 A141593 * A227491 A277943 A251945

Adjacent sequences: A221012 A221013 A221014 * A221016 A221017 A221018

Keyword

nonn,easy

Author

Emeric Deutsch, Dec 29 2012

Status

approved