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A (4,-8) Somos-4 sequence.
3

%I #8 Sep 08 2022 08:45:53

%S 1,2,4,-16,-256,-3072,-81920,-524288,184549376,20401094656,

%T 3848290697216,932385860354048,-229683580995895296,

%U -514202991054653751296,-608004684669466821263360,-1669526556887802890269229056,-2074787505842297340730932199424,33552176086840775798814740439891968

%N A (4,-8) Somos-4 sequence.

%C Hankel transform of A178076.

%H G. C. Greubel, <a href="/A178077/b178077.txt">Table of n, a(n) for n = 0..94</a>

%F a(n) = (4*a(n-1)*a(n-3) - 8*a(n-2)^2)/a(n-4), n>=4.

%t RecurrenceTable[{a[n] == (4*a[n-1]*a[n-3] -8*a[n-2]^2)/a[n-4], a[0] == 1, a[1] == 2, a[2] == 4, a[3] == -16}, a, {n, 0, 30}] (* _G. C. Greubel_, Sep 18 2018 *)

%o (PARI) m=30; v=concat([1,2,4,-16], vector(m-4)); for(n=5, m, v[n] = ( 4*v[n-1]*v[n-3] -8*v[n-2]^2)/v[n-4]); v \\ _G. C. Greubel_, Sep 18 2018

%o (Magma) I:=[1,2,4,-16]; [n le 4 select I[n] else (4*Self(n-1)*Self(n-3) - 8*Self(n-2)^2)/Self(n-4): n in [1..30]]; // _G. C. Greubel_, Sep 18 2018

%K easy,sign

%O 0,2

%A _Paul Barry_, May 19 2010

%E More terms from _G. C. Greubel_, Sep 18 2018