A305163 a(n) = 24*2^n - 18.

6, 30, 78, 174, 366, 750, 1518, 3054, 6126, 12270, 24558, 49134, 98286, 196590, 393198, 786414, 1572846, 3145710, 6291438, 12582894, 25165806, 50331630, 100663278, 201326574, 402653166, 805306350, 1610612718, 3221225454, 6442450926, 12884901870, 25769803758, 51539607534, 103079215086, 206158430190

Offset

0,1

Comments

a(n) is the number of vertices in the second type dendrimer nanostar NS2[n], defined pictorially in the Chen et al. reference (Fig. 1).

Links

Colin Barker, Table of n, a(n) for n = 0..1000

S. Chen and J. Yang, Second-order and third-order connectivity indices of dendrimer nanostars, International Mathematical Forum, 6, No, 5, 2011, 223-228.

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

Formula

G.f.: 6*(1+2*x)/((1-x)*(1-2*x)). - Vincenzo Librandi, May 27 2018

a(n) = 3*a(n-1) - 2*a(n-2) for n>1. - Colin Barker, May 27 2018

Maple

seq(24*2^n-18, n=0..40);

Mathematica

Table[24 2^n - 18, {n, 0, 33}] (* Vincenzo Librandi, May 27 2018 *)

Prog

(Magma) [24*2^n - 18: n in [0..33]]; // Vincenzo Librandi, May 27 2018
(PARI) Vec(6*(1 + 2*x) / ((1 - x)*(1 - 2*x)) + O(x^50)) \\ Colin Barker, May 27 2018

Crossrefs

Cf. A305164, A305165, A305166.

Sequence in context: A199130 A152743 A215906 * A038039 A258903 A050972

Adjacent sequences: A305160 A305161 A305162 * A305164 A305165 A305166

Keyword

nonn,easy

Author

Emeric Deutsch, May 27 2018

Status

approved