A227487 The hyper-Wiener index of the nanostar dendrimer defined pictorially as G[n] in the M. H. Khalifeh et al. reference.

34255, 398665, 3470157, 25438869, 166187685, 999925445, 5660148997, 30581012869, 159315487365, 806202248325, 3984535138437, 19312921409669, 92094055975045, 433117479708805, 2012917990713477, 9259384642267269, 42212038923118725, 190920673305290885, 857470623117994117, 3827025150533953669

Offset

0,1

Comments

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

Links

Table of n, a(n) for n=0..19.

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.

Formula

a(n) = -6011+2^n*(-111166-5960*n+7000*n^2)+4^n*(151432-35200*n+40000*n^2).

G.f.: (34255 -252180*z + 1033772*z^2 -2480544*z^3+3259584*z^4-2547712*z^5+790528*z^6)/((1-z)*(1-2*z)^3*(1-4*z)^3).

Maple

a := proc (n) options operator, arrow: -6011+2^n*(-111166-5960*n+7000*n^2)+4^n*(151432-35200*n+40000*n^2) end proc: seq(a(n), n = 0 .. 20);

Crossrefs

Cf. A227486

Sequence in context: A234820 A182292 A206214 * A204411 A238927 A236796

Adjacent sequences: A227484 A227485 A227486 * A227488 A227489 A227490

Keyword

nonn

Author

Emeric Deutsch, Jul 13 2013

Status

approved