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A (4,-5) Somos-4 sequence.
3

%I #7 Sep 08 2022 08:45:50

%S 1,-1,-9,-41,-241,-271,27329,651521,18425809,399122991,-24055184809,

%T -3943757411849,-498726356978849,-74609317288333151,

%U 2771780972000481601,8459493968101503667649,5139175203350482789079649

%N A (4,-5) Somos-4 sequence.

%C Hankel transform of A143013.

%H G. C. Greubel, <a href="/A171422/b171422.txt">Table of n, a(n) for n = 0..109</a>

%F a(n) = (4*a(n-1)*a(n-3) - 5*a(n-2)^2)/a(n-4), n>=3.

%t RecurrenceTable[{a[n] == (4*a[n-1]*a[n-3] -5*a[n-2]^2)/a[n-4], a[0] == 1, a[1] == -1, a[2] == -9, a[3] == -41}, a, {n, 0, 30}] (* _G. C. Greubel_, Sep 18 2018 *)

%o (PARI) m=30; v=concat([1,-1,-9,-41], vector(m-4)); for(n=5, m, v[n] = ( 4*v[n-1]*v[n-3] -5*v[n-2]^2)/v[n-4]); v \\ _G. C. Greubel_, Sep 18 2018

%o (Magma) I:=[1,-1,-9,-41]; [n le 4 select I[n] else (4*Self(n-1)*Self(n-3) -5*Self(n-2)^2)/Self(n-4): n in [1..30]]; // _G. C. Greubel_, Sep 18 2018

%K easy,sign

%O 0,3

%A _Paul Barry_, Dec 08 2009