A304168 a(n) = 2*3^n - 2^(n-1) (n>=1).

5, 16, 50, 154, 470, 1426, 4310, 12994, 39110, 117586, 353270, 1060834, 3184550, 9557746, 28681430, 86060674, 258214790, 774709906, 2324260790, 6973044514, 20919657830, 62760022066, 188282163350, 564850684354, 1694560441670, 5083698102226, 15251127861110, 45753450692194, 137260486294310, 411781727318386

Offset: 1

Author

Emeric Deutsch, May 10 2018

Keywords

• nonn
• easy

Comments

For n>=2, a(n) is the number of edges of the Sierpinski Gasket Rhombus graph SR(n) (see Theorem 2.1 in the D. Antony Xavier et al. reference).

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• D. Antony Xavier, M. Rosary, and Andrew Arokiaraj, Topological properties of Sierpinski Gasket Rhombus graphs, International J. of Mathematics and Soft Computing, 4, No. 2, 2014, 95-104.
• Index entries for linear recurrences with constant coefficients, signature (5,-6).

Crossrefs

Cf. A304167, A304169, A304170.

Programs

GAP

List([1..35],n->2*3^n-2^(n-1)); # Muniru A Asiru, May 10 2018

Maple

seq(2*3^n-2^(n-1), n = 1 .. 40);

PARI

Vec(x*(5 - 9*x) / ((1 - 2*x)*(1 - 3*x)) + O(x^30)) \\ Colin Barker, May 10 2018

Formula

From Colin Barker, May 10 2018: (Start)

G.f.: x*(5 - 9*x) / ((1 - 2*x)*(1 - 3*x)).

a(n) = 5*a(n-1) - 6*a(n-2) for n>2.

(End)