A058896 a(n) = 4^n - 4.

-3, 0, 12, 60, 252, 1020, 4092, 16380, 65532, 262140, 1048572, 4194300, 16777212, 67108860, 268435452, 1073741820, 4294967292, 17179869180, 68719476732, 274877906940, 1099511627772, 4398046511100, 17592186044412, 70368744177660, 281474976710652, 1125899906842620

Offset: 0

Author

Henry Bottomley, Jan 08 2001

Keywords

• sign
• easy

Links

• Harry J. Smith, Table of n, a(n) for n = 0..500
• Mattia Fregola, Elementary Cellular Automata Rule 1 generating OEIS sequence A277799, A058896, A141725, A002450
• Index entries for linear recurrences with constant coefficients, signature (5, -4).

Crossrefs

Cf. A000302, A000918, A002450, A024036, A052548, A058809, A141725, A277799.

Programs

GAP

List([0..25],n->4^n-4); # Muniru A Asiru, Mar 09 2018

Maple

seq(4^n-4,n=0..25); # Muniru A Asiru, Mar 09 2018

Mathematica

Array[4^# - 4 &, 26, 0]  (* Michael De Vlieger, Feb 18 2018 *)

PARI

a(n) = { 4^n - 4 } \\ Harry J. Smith, Jun 23 2009

Formula

a(n) = A000302(n) - 4 = 4*a(n-1) + 12 = 4*A024036(n-1) = 12*A002450(n-1).

G.f.: 3*(5*x - 1)/(1 - x)/(1 - 4*x).

a(n) = A000918(n)*A052548(n). - Reinhard Zumkeller, Feb 14 2009

From Elmo R. Oliveira, Nov 16 2023 (Start)

a(n) = 5*a(n-1) - 4*a(n-2) for n > 1.

E.g.f.: exp(4*x) - 4*exp(x). (End)