A121883 a(n) = (2*a(n-1)*a(n-3) + a(n-2)^2)/a(n-4), with a(1)=..=a(4)=1.

1, 1, 1, 1, 3, 7, 23, 187, 1049, 11889, 241169, 3461609, 133910987, 6440667383, 259246821927, 32041224742643, 3584042412456241, 447926142061771361, 160270294066699831201, 42116645114696072883921, 17694226961557153345377043, 16622226330147665886966252007

Offset

1,5

Links

G. C. Greubel, Table of n, a(n) for n = 1..118

A. N. W. Hone, Algebraic curves, integer sequences and a discrete Painlevé transcendent, arXiv:0807.2538 [nlin.SI], 2008; Proceedings of SIDE 6, Helsinki, Finland, 2004.

Maple

a:= proc(n) option remember;
      if n < 5 then 1
    else (2*a(n-1)*a(n-3) + a(n-2)^2)/a(n-4)
      fi;
    end proc:
seq(a(n), n = 1..30); # G. C. Greubel, Oct 08 2019

Mathematica

a[n_]:= a[n]= If[n<5, 1, (2*a[n-1]a[n-3] + a[n-2]^2)/a[n-4]]; Table[a[n], {n, 30}]
RecurrenceTable[{a[1]==a[2]==a[3]==a[4]==1, a[n]==(2a[n-1]a[n-3]+ a[n-2]^2)/ a[n-4]}, a, {n, 20}] (* Harvey P. Dale, May 27 2014 *)

Prog

(PARI) my(m=30, v=concat([1, 1, 1, 1], vector(m-4))); for(n=5, m, v[n] = (2*v[n-1]*v[n-3] + v[n-2]^2)/v[n-4]); v \\ G. C. Greubel, Oct 08 2019
(Magma) [n lt 5 select 1 else (2*Self(n-1)*Self(n-3) + Self(n-2)^2)/Self(n-4): n in [1..30]]; // G. C. Greubel, Oct 08 2019
(Sage)
@CachedFunction
def a(n):
    if (n<5): return 1
    else: return (2*a(n-1)*a(n-3) + a(n-2)^2)/a(n-4)
[a(n) for n in (1..30)] # G. C. Greubel, Oct 08 2019
(GAP) a:=[1, 1, 1, 1];; for n in [5..30] do a[n]:=(2*a[n-1]*a[n-3] + a[n-2]^2)/a[n-4]; od; a; # G. C. Greubel, Oct 08 2019

Crossrefs

Cf. A006720, A014125, A095708, A121881.

Sequence in context: A329875 A048721 A113824 * A262264 A060235 A343815

Adjacent sequences: A121880 A121881 A121882 * A121884 A121885 A121886

Keyword

nonn

Author

Roger L. Bagula, Sep 09 2006

Extensions

Edited by N. J. A. Sloane, Sep 15 2006

More terms added by G. C. Greubel, Oct 08 2019

Status

approved