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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
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.
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
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jul 21 2013
STATUS
approved

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Last modified March 4 04:21 EST 2024. Contains 370522 sequences. (Running on oeis4.)