OFFSET
1,1
COMMENTS
For n>=2, a(n) is the number of vertices 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 (6,-11,6).
FORMULA
From Colin Barker, May 10 2018: (Start)
G.f.: x*(4 - 15*x + 15*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)).
a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) for n>3.
(End)
a(n) = A083313(n)+2. - R. J. Mathar, Jul 24 2022
MAPLE
seq(3^n-2^(n-1)+2, n = 1 .. 40);
PROG
(PARI) Vec(x*(4 - 15*x + 15*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)) + O(x^30)) \\ Colin Barker, May 10 2018
(GAP) List([1..40], n->3^n-2^(n-1)+2); # Muniru A Asiru, May 10 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 10 2018
STATUS
approved