OFFSET
0,1
COMMENTS
a(n) is the second Zagreb index of the phenylazomethine dendrimer G[n] defined pictorially in the Yarahmadi references. The second Zagreb index of a simple connected graph is the sum of the degree products d(i)d(j) over all edges ij of the graph.
The M-polynomial of the dendrimer NSB[n] is M(NSB[n], x, y) = 9*2^n*x*y^4 + (24*2^n - 12)*x^2*y^2 + (48*2^n -24)*x^2*y^3 +(15*2^n-9)*x^3*y^3+3*2^n*x^3*y^4.
LINKS
E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
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 (3,-2).
FORMULA
O.g.f.: 3*(106 - 15*x)/((1 - x)*(1 - 2*x)).
E.g.f.: 3*(-91 + 197*exp(x))*exp(x).
a(n) = 3*a(n-1) - 2*a(n-2).
MAPLE
seq(591*2^n-273, n=0..35);
MATHEMATICA
Table[591 2^n - 273, {n, 0, 35}] (* Vincenzo Librandi, Nov 16 2016 *)
PROG
(Magma) [591*2^n-273: n in [0..35]]; // Vincenzo Librandi, Nov 16 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Nov 15 2016
EXTENSIONS
Edited by Bruno Berselli, Nov 16 2016
STATUS
approved