A227486 The Wiener index of the nanostar dendrimer defined pictorially as G[n] in the M. H. Khalifeh et al. reference.

5298, 39854, 251046, 1422550, 7507638, 37673334, 182185206, 856903670, 3945369078, 17864129014, 79813259766, 352738009590, 1545019376118, 6716624699894, 29013289140726, 124641612792310, 532923049312758, 2269124503273974, 9626239798084086, 40703952922083830, 171611842722922998

Offset

0,1

Comments

a(0) and a(1) have been checked by the direct computation of the Wiener index (using Maple).

Links

Matthew House, Table of n, a(n) for n = 0..1640

M. K. Khalifeh, H. Yousefi-Azari, and A. R. Ashrafi, The Szeged and Wiener numbers of water soluble polyaryl ether dendrimer nanostars, Digest J. Nanomaterials and Biostructures, 4, 2009, 63-66.

Index entries for linear recurrences with constant coefficients, signature (13,-64,148,-160,64).

Formula

a(n) = 502 + 2^(n)*(2800*n + 8716) + 4^(n)*(8000*n - 3920).

G.f.: 2*(2649 - 14510*z + 36008*z^2 - 37248*z^3 + 15360*z^4)/((1-z)*(1-2*z)^2*(1-4*z)^2).

a(n) = 13*a(n-1) - 64*a(n-2) + 148*a(n-3) - 160*a(n-4) + 64*a(n-5). - Matthew House, Nov 01 2016

Maple

a := proc (n) options operator, arrow: 502+2^n*(2800*n+8716)+4^n*(8000*n-3920) end proc: seq(a(n), n = 0 .. 20);

Crossrefs

Cf. A227487

Sequence in context: A178027 A053397 A300365 * A252189 A204838 A212078

Adjacent sequences: A227483 A227484 A227485 * A227487 A227488 A227489

Keyword

nonn

Author

Emeric Deutsch, Jul 13 2013

Status

approved