OFFSET
0,1
COMMENTS
a(n) is the second Zagreb index of the phenylazomethine dendrimer G[n], defined pictorially in the Golriz et al. reference (Fig. 1). 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 G[n] is M(G[n],x,y) = (24*2^n - 8)*x^2*y^2 + (24*2^n - 16)*x^2*y^3 + (12*2^n -12)*x^3*y^3 +4*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.
M. Golriz, M. R. Darafsheh, and M. H. Khalifeh, The Wiener, Szeged and PI-indices of a phenylazomethine dendrimer, Digest J. Nanomaterials and Biostructures, 6, No. 4, 2011, 1545-1549.
Index entries for linear recurrences with constant coefficients, signature (3,-2).
FORMULA
O.g.f.: 4*(40 + 7*x)/((1 - x)*(1 - 2*x)).
E.g.f.: 4*(-47 + 87*exp(x))*exp(x).
a(n) = 3*a(n-1) - 2*a(n-2).
MAPLE
seq(348*2^n-188, n = 0..35);
MATHEMATICA
Table[348 2^n - 188, {n, 0, 30}] (* Bruno Berselli, Nov 15 2016 *)
LinearRecurrence[{3, -2}, {160, 508}, 30] (* Harvey P. Dale, Jul 22 2021 *)
PROG
(Magma) [348*2^n-188: n in [0..40]]; // Vincenzo Librandi, Nov 15 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Nov 15 2016
STATUS
approved