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A305165
a(n) = 136*2^n - 112.
3
24, 160, 432, 976, 2064, 4240, 8592, 17296, 34704, 69520, 139152, 278416, 556944, 1114000, 2228112, 4456336, 8912784, 17825680, 35651472, 71303056, 142606224, 285212560, 570425232, 1140850576, 2281701264, 4563402640, 9126805392, 18253610896, 36507221904, 73014443920, 146028887952, 292057776016, 584115552144
OFFSET
0,1
COMMENTS
a(n) is the first Zagreb index of the second type dendrimer nanostar NS2[n], defined pictorially in the Chen et al. reference (Fig. 1).
The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternatively, it is the sum of the degree sums d(i) + d(j) over all edges ij of the graph.
The M-polynomial of NS2[n] is M(NS2[n];x,y) = 2*(4*2^n-1)*x^2*y^2 + 16*(2*n - 1)*x^2*y^3 + 4*(2^n - 1)*x^3*y^3 (n>=0).
LINKS
S. Chen and J. Yang, Second-order and third-order connectivity indices of dendrimer nanostars, International Mathematical Forum, 6, No, 5, 2011, 223-228.
E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
FORMULA
G.f.: 8*(3 + 11*x)/((1 - x)*(1 - 2*x)). - Vincenzo Librandi, May 27 2018
MAPLE
seq(136*2^n-112, n = 0 .. 40);
MATHEMATICA
Table[136 2^n - 112, {n, 0, 33}] (* Vincenzo Librandi, May 27 2018 *)
LinearRecurrence[{3, -2}, {24, 160}, 40] (* Harvey P. Dale, Jan 30 2023 *)
PROG
(Magma) [136*2^n - 112: n in [0..33]]; // Vincenzo Librandi, May 27 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 27 2018
STATUS
approved