Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #9 Sep 08 2022 08:45:51
%S 1,2,-3,1,11,-16,-35,-129,299,-386,-3977,8063,42489,269344,-1000009,
%T 3727745,47166649,-123526014,-1764203419,-18228952703,113727892147,
%U -1065812586544,-18344075481339,52130069331199,2470319425874195
%N A (1,1) Somos-4 sequence.
%C Hankel transform of A174013.
%H G. C. Greubel, <a href="/A174017/b174017.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>3.
%t RecurrenceTable[{a[n] == (a[n-1]*a[n-3] +a[n-2]^2)/a[n-4], a[0] == 1, a[1] == 2, a[2] == -3, a[3] == 1}, a, {n, 0, 150}] (* _G. C. Greubel_, Sep 18 2018 *)
%t nxt[{a_,b_,c_,d_}]:={b,c,d,(b*d+c^2)/a}; NestList[nxt,{1,2,-3,1},30][[All,1]] (* _Harvey P. Dale_, Jun 21 2022 *)
%o (PARI) m=30; v=concat([1,2,-3,1], vector(m-4)); for(n=5, m, v[n] = ( v[n-1]*v[n-3] +v[n-2]^2)/v[n-4]); v \\ _G. C. Greubel_, Sep 18 2018
%o (Magma) I:=[1,2,-3,1]; [n le 4 select I[n] else (Self(n-1)*Self(n-3) + 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_, Mar 05 2010