OFFSET
0,1
COMMENTS
a(0) has been checked by the direct computation of the Wiener index (using Maple).
LINKS
Z. Yarahmadi, Eccentric connectivity and augmented eccentric connectivity indices of N-branches phenylacetylenes nanostar dendrimers, Iranian J. Math. Chem., 1, No. 2, 2010, 105-110.
Z. Yarahmadi and G. H. Fath-Tabar, The Wiener, Szeged, PI, Vertex PI, the first and second Zagreb indices of N-branched phenylacetylenes dendrimers, MATCH: Commun. Math. Comput. Chem, 65 (2011) 201-208.
Index entries for linear recurrences with constant coefficients, signature (11,-42,64,-32).
FORMULA
a(n) = -9369 + 85725*2^n - 65772*4^n +68121*n*4^n (agrees with Theorem 3 of the Yarahmadi et al. reference).
G.f.: 27*(392+2039*x+716*x^2-24*x^3)/((1-x)*(1-2*x)*(1-4*x)^2). [Bruno Berselli, Apr 06 2013]
MAPLE
a := proc (n) options operator, arrow: -9369+68121*4^n*n+85725*2^n-65772*4^n end proc: seq(a(n), n = 0 .. 18);
MATHEMATICA
CoefficientList[Series[27 (392 + 2039 x + 716 x^2 - 24 x^3)/((1 - x) (1 - 2 x) (1 - 4 x)^2), {x, 0, 20}], x] (* Bruno Berselli, Apr 06 2013 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Apr 06 2013
STATUS
approved