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A227702 The hyper-Wiener index of the nanostar dendrimer defined pictorially in Fig. 1 of the Iranmanesh et al. reference. 2
449908, 1096118, 3588202, 14360018, 64595362, 307414082, 1492075906, 7247514626, 34935347458, 166607364866, 785654642434, 3665131036418, 16929529343746, 77501591179010, 351950298746626, 1586770938400514, 7107632205434626, 31651156830097154 (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 hyper-Wiener index (using Maple).
LINKS
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
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jul 21 2013
STATUS
approved

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Last modified April 15 12:18 EDT 2024. Contains 371686 sequences. (Running on oeis4.)