A227701 The Wiener index of the nanostar dendrimer defined pictorially in Fig. 1 of the Iranmanesh et al. reference.

48279, 96987, 255171, 834771, 3170163, 13124019, 56647731, 248434995, 1092754227, 4792876851, 20915808051, 90764867379, 391736497971, 1682238527283, 7191380186931, 30617911318323, 129886929049395, 549220992440115, 2315602753509171, 9737340299794227

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