OFFSET
1,5
COMMENTS
A variation of a Somos-4 sequence with a(n-2)^3 in place of a(n-2)^2.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..21
FORMULA
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
From Jon E. Schoenfield, May 12 2019: (Start)
It appears that, for n >= 1,
a(n) = ceiling(e^(c0*phi^n + d0/phi^n)) if n is even,
ceiling(e^(c1*phi^n + d1/phi^n)) if n is odd,
where
phi = (1 + sqrt(5))/2,
c0 = 0.087172479898911051233710515749226588954735607680...
c1 = 0.087662681482404614007222542134598226046349621976...
d0 = -9.574280373370101810186207466479291633433387765559...
d1 = -4.425515288739040257644546086989175506652492968654...
(End)
MATHEMATICA
Nest[Append[#, (#[[-1]]*#[[-3]] + #[[-2]]^3)/#[[-4]] ] &, {1, 1, 1, 1}, 11] (* Michael De Vlieger, May 12 2019 *)
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 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Jul 28 2002
STATUS
approved