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A227701 The Wiener index of the nanostar dendrimer defined pictorially in Fig. 1 of the Iranmanesh et al. reference. 2
48279, 96987, 255171, 834771, 3170163, 13124019, 56647731, 248434995, 1092754227, 4792876851, 20915808051, 90764867379, 391736497971, 1682238527283, 7191380186931, 30617911318323, 129886929049395, 549220992440115, 2315602753509171, 9737340299794227 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

A. Iranmanesh, N. A. Gholami, Computing the Szeged index of two type dendrimer nanostars, Croatica Chemica Acta, 81, No. 2, 2008, 299-303.

T. Tada, D. Nozaki, M. Kondo, K. Yoshizawa, Molecular orbital interactions in the nanostar dendrimer, J. Phys. Chem. B 107, 2003, 14204-14210.

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

FORMULA

a(n) = 22323 + 2^n*(9018 + 2664*n) + 4^n*(216 + 432*n).

G.f.: 3*x*(16093 - 176880*x + 694732*x^2 - 1140192*x^3 + 673216*x^4)/((1 - x)*(1 - 2*x)^2*(1 - 4*x)^2).

a(n) = 13*a(n-1) - 64*a(n-2) + 148*a(n-3) - 160*a(n-4) + 64*a(n-5) for n>5. - Colin Barker, May 30 2018

MAPLE

a := proc (n) options operator, arrow: 22323+2^n*(9018+2664*n)+4^n*(216+432*n) end proc: seq(a(n), n = 1 .. 20);

PROG

(PARI) Vec(3*x*(16093 - 176880*x + 694732*x^2 - 1140192*x^3 + 673216*x^4) / ((1 - x)*(1 - 2*x)^2*(1 - 4*x)^2) + O(x^20)) \\ Colin Barker, May 30 2018

CROSSREFS

Cf. A227702.

Sequence in context: A254724 A186592 A221556 * A253494 A253501 A253455

Adjacent sequences:  A227698 A227699 A227700 * A227702 A227703 A227704

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Jul 21 2013

STATUS

approved

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Last modified October 26 11:59 EDT 2021. Contains 348267 sequences. (Running on oeis4.)