A227493 The hyper-Wiener index of the nanostar dendrimer D_n.

42, 14652, 376080, 4717944, 42247752, 311654376, 2030475048, 12146472360, 68316332712, 366865702056, 1900861968552, 9573539690664, 47121333848232, 227582442154152, 1081872982370472, 5074283412646056, 23526766452271272, 107995434142918824, 491414463894251688, 2218905516729428136

Offset

1,1

Comments

D_n is defined pictorially as NS2[n] in the Chen et al. reference.

a(1) and a(2) have been checked by the direct computation of the Wiener index (using Maple).

Links

Table of n, a(n) for n=1..20.

S. Chen and J. Yang, Second-order and third-order connectivity indices of dendrimer nanostars, International Mathematical Forum, 6, No, 5, 2011, 223-228.

Index entries for linear recurrences with constant coefficients, signature (19,-150,636,-1560,2208,-1664,512).

Formula

a(n) = - 5976 + 2^n*(7056*n^2 - 33264*n - 213990) + 4^n*(28244*n^2 - 122976*n + 220008).

G.f.: 6*(7 + 2309*x + 17332*x^2 - 42748*x^3 - 39056*x^4 + 36032*x^5 -768*x^6)/((1-x)*(1-2*x)^3*(1-4*x)^3).

Maple

a := proc (n) options operator, arrow: -5976+2^n*(7056*n^2-33264*n-213990)+4^n*(28224*n^2-122976*n+220008) end proc: seq(a(n), n = 0 .. 22);

Crossrefs

Cf. A227492.

Sequence in context: A289540 A275453 A268552 * A095423 A174766 A265191

Adjacent sequences: A227490 A227491 A227492 * A227494 A227495 A227496

Keyword

nonn,easy

Author

Emeric Deutsch, Jul 17 2013

Status

approved