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A227490
The Wiener index of the nanostar dendrimer D_n, defined pictorially in the Ghorbani et al. references and recursively in the Deutsch et al. reference.
2
666, 35325, 412443, 3099663, 19013175, 104225031, 533102247, 2604327399, 12319287399, 56913753447, 258258898791, 1155566158695, 5112617020263, 22412337970023, 97497752214375, 421386451835751, 1811131262622567, 7746874238425959
OFFSET
1,1
COMMENTS
a(1) has been checked by the direct computation of the Wiener index (using Maple).
In the Ghorbani & Songhori reference the formula for the Wiener index (p. 62) contains some errors.
The Deutsch et al. reference contains also the Hosoya polynomial of D_n.
LINKS
E. Deutsch, S. Klavzar, Computing the Hosoya polynomial of graphs from primary subgraphs, MATCH Commun. Math. Comput. Chem., 70, 2013, 627-644.
M. Ghorbani, A. Mohammadi, F. Madadi, Some topological indices of nanostar dendrimers, Optoelectronics and Adv. Materials - Rapid Comm., 4, 2010, 1871-1873.
M. Ghorbani and M. Songhori, Some topological indices of nanostar dendrimers, Iranian J. Math. Chemistry, 1, No. 2, 2010, 57-65.
FORMULA
a(n) = - 9369 + 56205*2^(n-1) - 75411*2^(2n-2) + 29241*2^(2n-2)*n.
G.f.: 9*x*(74 + 3111*x + 5760*x^2 + 424*x^3)/((1-x)*(1-2*x)*(1-4*x)^2).
a(n) = 11*a(n-1) - 42*a(n-2) + 64*a(n-3) - 32*a(n-4) for n>4. - Colin Barker, Jun 15 2018
MAPLE
a := proc (n) options operator, arrow: -9369+56205*2^(n-1)-75411*2^(2*n-2)+29241*2^(2*n-2)*n end proc: seq(a(n), n = 1 .. 22);
MATHEMATICA
Table[-9369+56205*2^(n-1)-75411*2^(2n-2)+29241*2^(2n-2) n, {n, 20}] (* or *) LinearRecurrence[{11, -42, 64, -32}, {666, 35325, 412443, 3099663}, 20] (* Harvey P. Dale, Dec 24 2017 *)
PROG
(GAP) List([1..20], n-> 29241*2^(2*n-2)*n-75411*2^(2*n-2)+56205*2^(n-1)-9369); # Muniru A Asiru, Jun 15 2018
(PARI) Vec(9*x*(74 + 3111*x + 5760*x^2 + 424*x^3)/((1-x)*(1-2*x)*(1-4*x)^2) + O(x^40)) \\ Colin Barker, Jun 15 2018
CROSSREFS
Cf. A227491.
Sequence in context: A104181 A221014 A057564 * A171114 A328551 A172922
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jul 16 2013
STATUS
approved