A304510 a(n) = 69*2^n - 42 (n>=1).

96, 234, 510, 1062, 2166, 4374, 8790, 17622, 35286, 70614, 141270, 282582, 565206, 1130454, 2260950, 4521942, 9043926, 18087894, 36175830, 72351702, 144703446, 289406934, 578813910, 1157627862, 2315255766, 4630511574, 9261023190, 18522046422, 37044092886, 74088185814, 148176371670, 296352743382, 592705486806

Offset

1,1

Comments

a(n) = number of edges of the dendrimer nanostar NS2[n], defined pictorially in Fig. 2 of the Madanshekaf reference.

References

A. Madanshekaf, The Randic index of some dendrimer nanostars, J. Appl. Math. & Informatics, 29, No. 5-6, 2011, 1075-1080.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

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

Formula

From Colin Barker, May 15 2018: (Start)

G.f.: 6*x*(16 - 9*x) / ((1 - x)*(1 - 2*x)).

a(n) = 3*a(n-1) - 2*a(n-2) for n>2.

(End)

Maple

seq(69*2^n-42, n = 1 .. 40);

Mathematica

Array[69*2^# - 42 &, 33] (* Michael De Vlieger, May 14 2018 *)

Prog

(GAP) List([1..40], n->69*2^n-42); # Muniru A Asiru, May 15 2018
(PARI) Vec(6*x*(16 - 9*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 15 2018

Crossrefs

Cf. A304509, A304511, A304512.

Sequence in context: A108609 A125511 A124106 * A268771 A202898 A202891

Adjacent sequences: A304507 A304508 A304509 * A304511 A304512 A304513

Keyword

nonn,easy

Author

Emeric Deutsch, May 14 2018

Status

approved