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A278131 a(n) = 591*2^n - 273. 1
318, 909, 2091, 4455, 9183, 18639, 37551, 75375, 151023, 302319, 604911, 1210095, 2420463, 4841199, 9682671, 19365615, 38731503, 77463279, 154926831, 309853935, 619708143, 1239416559, 2478833391, 4957667055, 9915334383, 19830669039, 39661338351 (list; graph; refs; listen; history; text; internal format)
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 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.
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
Cf. A278130.
Sequence in context: A323328 A045272 A359012 * A075153 A204835 A281078
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Nov 15 2016
EXTENSIONS
Edited by Bruno Berselli, Nov 16 2016
STATUS
approved

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Last modified June 15 18:41 EDT 2024. Contains 373410 sequences. (Running on oeis4.)