|
%I #40 Jul 06 2019 15:02:26
%S 1,1,1,1,2,3,11,49,739,41926,36876163,1504578225617,
%T 67856786028033600651,81238311359334144709516343054051,
%U 8472940010945536421401513734595877223414710434640386
%N a(1) = a(2) = a(3) = a(4) = 1 and a(n) = (a(n-1)*a(n-3) + a(n-2)^3)/a(n-4) for n >= 5.
%C A variation of a Somos-4 sequence with a(n-2)^3 in place of a(n-2)^2.
%H Seiichi Manyama, <a href="/A072876/b072876.txt">Table of n, a(n) for n = 1..21</a>
%F Lim_{n->infinity} (log(log a(n)))/n = log((1+sqrt(5))/2) or about 0.48. See A002390. However, convergence is extremely slow. - _Andrew Hone_, Nov 15 2005
%F From _Jon E. Schoenfield_, May 12 2019: (Start)
%F It appears that, for n >= 1,
%F a(n) = ceiling(e^(c0*phi^n + d0/phi^n)) if n is even,
%F ceiling(e^(c1*phi^n + d1/phi^n)) if n is odd,
%F where
%F phi = (1 + sqrt(5))/2,
%F c0 = 0.087172479898911051233710515749226588954735607680...
%F c1 = 0.087662681482404614007222542134598226046349621976...
%F d0 = -9.574280373370101810186207466479291633433387765559...
%F d1 = -4.425515288739040257644546086989175506652492968654...
%F (End)
%t Nest[Append[#, (#[[-1]]*#[[-3]] + #[[-2]]^3)/#[[-4]] ] &, {1, 1, 1, 1}, 11] (* _Michael De Vlieger_, May 12 2019 *)
%t RecurrenceTable[{a[1]==a[2]==a[3]==a[4]==1,a[n]==(a[n-1]a[n-3]+a[n-2]^3)/ a[n-4]},a,{n,20}] (* _Harvey P. Dale_, May 15 2019 *)
%Y Cf. A002390, A006720, A072877, A111459.
%K easy,nonn
%O 1,5
%A _Benoit Cloitre_, Jul 28 2002
| 