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%I #29 Nov 16 2023 19:03:43
%S -3,0,12,60,252,1020,4092,16380,65532,262140,1048572,4194300,16777212,
%T 67108860,268435452,1073741820,4294967292,17179869180,68719476732,
%U 274877906940,1099511627772,4398046511100,17592186044412,70368744177660,281474976710652,1125899906842620
%N a(n) = 4^n - 4.
%H Harry J. Smith, <a href="/A058896/b058896.txt">Table of n, a(n) for n = 0..500</a>
%H Mattia Fregola, <a href="https://docs.google.com/spreadsheets/d/1629UXZ07lVK1-LVR0T7u1RDVKeW4f55K688CAtS5maw/edit?usp=sharing">Elementary Cellular Automata Rule 1 generating OEIS sequence A277799, A058896, A141725, A002450</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5, -4).
%F a(n) = A000302(n) - 4 = 4*a(n-1) + 12 = 4*A024036(n-1) = 12*A002450(n-1).
%F G.f.: 3*(5*x - 1)/(1 - x)/(1 - 4*x).
%F a(n) = A000918(n)*A052548(n). - _Reinhard Zumkeller_, Feb 14 2009
%F From _Elmo R. Oliveira_, Nov 16 2023 (Start)
%F a(n) = 5*a(n-1) - 4*a(n-2) for n > 1.
%F E.g.f.: exp(4*x) - 4*exp(x). (End)
%p seq(4^n-4,n=0..25); # _Muniru A Asiru_, Mar 09 2018
%t Array[4^# - 4 &, 26, 0] (* _Michael De Vlieger_, Feb 18 2018 *)
%o (PARI) { f=1; for (n = 0, 500, write("b058896.txt", n, " ", f-4); f*=4; ) } \\ _Harry J. Smith_, Jun 23 2009
%o (GAP) List([0..25],n->4^n-4); # _Muniru A Asiru_, Mar 09 2018
%Y Cf. A000302, A000918, A002450, A024036, A052548, A058809, A141725, A277799.
%K sign,easy
%O 0,1
%A _Henry Bottomley_, Jan 08 2001
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