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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. 3
1, 1, 1, 1, 2, 3, 11, 49, 739, 41926, 36876163, 1504578225617, 67856786028033600651, 81238311359334144709516343054051, 8472940010945536421401513734595877223414710434640386 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 14 10:22 EST 2019. Contains 329111 sequences. (Running on oeis4.)