login
A304168
a(n) = 2*3^n - 2^(n-1) (n>=1).
2
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
1,1
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
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.
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)
MAPLE
seq(2*3^n-2^(n-1), n = 1 .. 40);
PROG
(PARI) Vec(x*(5 - 9*x) / ((1 - 2*x)*(1 - 3*x)) + O(x^30)) \\ Colin Barker, May 10 2018
(GAP) List([1..35], n->2*3^n-2^(n-1)); # Muniru A Asiru, May 10 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 10 2018
STATUS
approved