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A305063
a(n) = 110*2^n + 118.
3
228, 338, 558, 998, 1878, 3638, 7158, 14198, 28278, 56438, 112758, 225398, 450678, 901238, 1802358, 3604598, 7209078, 14418038, 28835958, 57671798, 115343478, 230686838, 461373558, 922746998, 1845493878, 3690987638, 7381975158, 14763950198, 29527900278, 59055800438, 118111600758, 236223201398
OFFSET
0,1
COMMENTS
a(n)(n>=0) is the second Zagreb index of the dendrimer graph K[n], defined pictorially in the Ghorbani et al. reference (see Figs. 9, 10, and 11).
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 K[n] is M(K[n]; x, y) = 2*2^n*x*y^3 + 2*(2^n + 2)*x^2*y^2 + (2^4*2^n -4)*x^2*y^3 + 14*x^3*y^3.
LINKS
E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
M. Ghorbani, K. Malekjani, and A. Khaki, Eccentric connectivity index of some dendrimer graphs, Iranian J. of Math. Chemistry, 3, Supplement 1, 2012, s7 - s18.
FORMULA
G.f.: (228 - 346*x)/((1 - 2*x)*(1 - x)). - Vincenzo Librandi, May 25 2018
a(n) = 3*a(n-1) - 2* a(n-2). - Vincenzo Librandi, May 25 2018
MAPLE
seq(110*2^n+118, n = 0 .. 40);
MATHEMATICA
Table[110 2^n + 118, {n, 0, 31}] (* Vincenzo Librandi, May 25 2018 *)
PROG
(Magma) [110*2^n+118: n in [0..40]]; // Vincenzo Librandi, May 25 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 24 2018
STATUS
approved