A227702 The hyper-Wiener index of the nanostar dendrimer defined pictorially in Fig. 1 of the Iranmanesh et al. reference.

449908, 1096118, 3588202, 14360018, 64595362, 307414082, 1492075906, 7247514626, 34935347458, 166607364866, 785654642434, 3665131036418, 16929529343746, 77501591179010, 351950298746626, 1586770938400514, 7107632205434626, 31651156830097154

Offset

1,1

Comments

a(1) and a(2) have been checked by the direct computation of the hyper-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 (19,-150,636,-1560,2208,-1664,512).

Formula

a(n) = 167682 + 2^n*(79709 + 24876*n + 3996*n^(2)) + 4^n*(13458 + 1512* n + 1296*n^(2)).

G.f.: 2*x*(224954 - 3726067*x + 25124080*x^2 - 87769804*x^3 + 167355376*x^4 -165722176*x^5 + 66777344*x^6)/((1-x)*(1-2*x)^3*(1-4*x)^3).

a(n) = 19*a(n-1) - 150*a(n-2) + 636*a(n-3) - 1560*a(n-4) + 2208*a(n-5) - 1664*a(n-6) + 512*a(n-7) for n>6. - Colin Barker, May 30 2018

Maple

a:= proc (n) options operator, arrow: 167682+2^n*(79709+24876*n+3996*n^2)+4^n*(13458+1512*n+1296*n^2) end proc: seq(aa(n), n = 1 .. 20);

Mathematica

LinearRecurrence[{19, -150, 636, -1560, 2208, -1664, 512}, {449908, 1096118, 3588202, 14360018, 64595362, 307414082, 1492075906}, 20] (* Harvey P. Dale, Dec 03 2023 *)

Prog

(PARI) Vec(2*x*(224954 - 3726067*x + 25124080*x^2 - 87769804*x^3 + 167355376*x^4 - 165722176*x^5 + 66777344*x^6) / ((1 - x)*(1 - 2*x)^3*(1 - 4*x)^3) + O(x^20)) \\ Colin Barker, May 30 2018

Crossrefs

Cf. A227701.

Sequence in context: A202569 A224635 A234231 * A210332 A209714 A203785

Adjacent sequences: A227699 A227700 A227701 * A227703 A227704 A227705

Keyword

nonn,easy

Author

Emeric Deutsch, Jul 21 2013

Status

approved