A072876 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.

1, 1, 1, 1, 2, 3, 11, 49, 739, 41926, 36876163, 1504578225617, 67856786028033600651, 81238311359334144709516343054051, 8472940010945536421401513734595877223414710434640386

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

Cf. A002390, A006720, A072877, A111459.

Sequence in context: A268285 A100701 A011365 * A184315 A020133 A086528

Adjacent sequences: A072873 A072874 A072875 * A072877 A072878 A072879

Keyword

easy,nonn

Author

Benoit Cloitre, Jul 28 2002

Status

approved