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a(n) = (2*a(n-1)*a(n-3) + a(n-2)^2)/a(n-4), with a(1)=..=a(4)=1.
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%I #18 Sep 08 2022 08:45:27

%S 1,1,1,1,3,7,23,187,1049,11889,241169,3461609,133910987,6440667383,

%T 259246821927,32041224742643,3584042412456241,447926142061771361,

%U 160270294066699831201,42116645114696072883921,17694226961557153345377043,16622226330147665886966252007

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

%H G. C. Greubel, <a href="/A121883/b121883.txt">Table of n, a(n) for n = 1..118</a>

%H A. N. W. Hone, <a href="http://arXiv.org/abs/0807.2538">Algebraic curves, integer sequences and a discrete Painlevé transcendent</a>, arXiv:0807.2538 [nlin.SI], 2008; Proceedings of SIDE 6, Helsinki, Finland, 2004.

%p a:= proc(n) option remember;

%p if n < 5 then 1

%p else (2*a(n-1)*a(n-3) + a(n-2)^2)/a(n-4)

%p fi;

%p end proc:

%p seq(a(n), n = 1..30); # _G. C. Greubel_, Oct 08 2019

%t 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}]

%t 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 *)

%o (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

%o (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

%o (Sage)

%o @CachedFunction

%o def a(n):

%o if (n<5): return 1

%o else: return (2*a(n-1)*a(n-3) + a(n-2)^2)/a(n-4)

%o [a(n) for n in (1..30)] # _G. C. Greubel_, Oct 08 2019

%o (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

%Y Cf. A006720, A014125, A095708, A121881.

%K nonn

%O 1,5

%A _Roger L. Bagula_, Sep 09 2006

%E Edited by _N. J. A. Sloane_, Sep 15 2006

%E More terms added by _G. C. Greubel_, Oct 08 2019