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A058896
a(n) = 4^n - 4.
7
-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
0,1
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)
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 *)
PROG
(PARI) { f=1; for (n = 0, 500, write("b058896.txt", n, " ", f-4); f*=4; ) } \\ Harry J. Smith, Jun 23 2009
(GAP) List([0..25], n->4^n-4); # Muniru A Asiru, Mar 09 2018
KEYWORD
sign,easy
AUTHOR
Henry Bottomley, Jan 08 2001
STATUS
approved