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%I #11 Sep 08 2022 08:45:51
%S 1,0,-1,-1,-1,-2,-1,3,7,8,25,37,-47,-318,-559,-2023,-7039,496,90431,
%T 314775,1139599,8007614,13512079,-154788437,-1247862041,-5097732072,
%U -56844671623,-290379801907,1403230649825,32188159859842
%N Hankel transform of A174399.
%C Essentially a (1,-1) Somos-4 sequence.
%H G. C. Greubel, <a href="/A174400/b174400.txt">Table of n, a(n) for n = 0..150</a>
%F a(n) = (a(n-1)*a(n-3) - a(n-2)^2)/a(n-4), n>=6.
%F a(n) = -a(2-n), a(n)*a(n+5) = a(n+1)*a(n+4) - 2*a(n+2)*a(n+3) for all n in Z. - _Michael Somos_, Sep 26 2018
%t nxt[{a_,b_,c_,d_}]:={b,c,d,(d*b-c^2)/a}; Join[{1,0},NestList[nxt,{-1,-1,-1,-2},30][[All,1]]] (* _Harvey P. Dale_, Sep 07 2017 *)
%t Join[{1, 0}, RecurrenceTable[{a[n] == (a[n-1]*a[n-3] -a[n-2]^2)/a[n-4], a[2] == -1, a[3] == -1, a[4] == -1, a[5] == -2}, a, {n, 2, 50}]] (* _G. C. Greubel_, Sep 25 2018 *)
%o (PARI) m=20; v=concat([-1,-1,-1,-2], vector(m-4)); for(n=5, m, v[n] = ( 100*v[n-1]*v[n-3] - 196*v[n-2]^2)/v[n-4]); concat([1,0], v) \\ _G. C. Greubel_, Sep 25 2018
%o (Magma) I:=[-1,-1,-1,-2]; [1,0] cat [n le 4 select I[n] else (Self(n-1)*Self(n-3) - Self(n-2)^2)/Self(n-4): n in [1..20]]; // _G. C. Greubel_, Sep 25 2018
%K easy,sign
%O 0,6
%A _Paul Barry_, Mar 18 2010
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