A166060 a(n) = 4*3^n - 3*2^n.

1, 6, 24, 84, 276, 876, 2724, 8364, 25476, 77196, 233124, 702444, 2113476, 6352716, 19082724, 57297324, 171990276, 516167436, 1548895524, 4647473004, 13943991876, 41835121356, 125511655524, 376547549484, 1129667814276, 3389053774476, 10167261986724, 30501987286764

Offset: 0

Author

Philippe Deléham, Oct 05 2009

Keywords

• nonn
• easy

Comments

Second binomial transform of A123932 = [1,4,4,4,4,4,4,4,...].

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• John Elias, Illustration of initial terms: Sierpinski-tetra-triangles
• Index entries for linear recurrences with constant coefficients, signature (5,-6).

Crossrefs

Cf. A082560, A123932, A217764, A257956.

Programs

Haskell

a166060 n = a166060_list !! n
a166060_list = map fst $ iterate (\(u, v) -> (3 * (u + v), 2 * v)) (1, 1)
-- Reinhard Zumkeller, Jun 09 2013

Magma

[4*3^n-3*2^n: n in [0..30]]; // Vincenzo Librandi, Dec 05 2012

Mathematica

CoefficientList[Series[(1+x)/((1-2x)*(1-3x)), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 05 2012 *)

PARI

a(n)=4*3^n-3<Charles R Greathouse IV, Jan 12 2012

Formula

a(n) = 5*a(n-1) - 6*a(n-2) for n > 1; a(0)= 1, a(1)= 6.

G.f.: (1+x)/(1-5x+6x^2).

a(n) = A217764(n,6). - Ross La Haye, Mar 27 2013

a(n) = Sum_{k = 1..2^n} A082560(n+1,k). - Reinhard Zumkeller, May 14 2015

E.g.f.: exp(2*x)*(4*exp(x) - 3). - Stefano Spezia, May 18 2024

Extensions

a(19) and a(22) corrected by Charles R Greathouse IV, Jan 12 2012