A305165 a(n) = 136*2^n - 112.

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

Table of n, a(n) for n=0..32.

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.

Index entries for linear recurrences with constant coefficients, signature (3,-2).

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

Cf. A305163, A305164, A305166.

Sequence in context: A240268 A231341 A186862 * A294110 A136380 A250323

Adjacent sequences: A305162 A305163 A305164 * A305166 A305167 A305168

Keyword

nonn,easy

Author

Emeric Deutsch, May 27 2018

Status

approved