%I
%S 1,1,1,4,3,19,67,40,1243,4299,25627,334324,627929,29742841,
%T 372632409,1946165680,128948361769,1488182579081,52394610324649,
%U 2333568937567764,5642424912729707,3857844273728205019
%N A (1,1) Somos4 sequence associated to the elliptic curve y^2 + x*y + y = x^3 + x^2 + x.
%C Hankel transform of the sequence with g.f. 1/(1x^2/(1x^2/(14x^2/(1+(3/16)x^2/(1(76/9)x^2/(1.... where 1,4,3/16,76/9,... are the xcoordinates of the multiples of (0,0).
%H G. C. Greubel, <a href="/A178417/b178417.txt">Table of n, a(n) for n = 1..156</a> (offset adapted by _Georg Fischer_, Jan 31 2019).
%F a(n) = (a(n1)*a(n3) + a(n2)^2)/a(n4), n>3.
%F a(n) = (1)^n*a(n) for all n in Z.  _Michael Somos_, Sep 17 2018
%e G.f. = x + x^2 + x^3 + 4*x^4  3*x^5 + 19*x^6  67*x^7 + ...  _Michael Somos_, Sep 17 2018
%t RecurrenceTable[{a[n] == (a[n1]*a[n3] +a[n2]^2)/a[n4], a[0] == 1, a[1] == 1, a[2] == 1, a[3] == 4}, a, {n, 0, 30}] (* _G. C. Greubel_, Sep 16 2018 *)
%o (PARI) m=30; v=concat([1,1,1,4], vector(m4)); for(n=5, m, v[n] = ( v[n1]*v[n3] +v[n2]^2)/v[n4]); v \\ _G. C. Greubel_, Sep 16 2018
%o (MAGMA) I:=[1,1,1,4]; [n le 4 select I[n] else (Self(n1)*Self(n3) + Self(n2)^2)/Self(n4): n in [1..30]]; // _G. C. Greubel_, Sep 16 2018
%K easy,sign
%O 1,4
%A _Paul Barry_, May 27 2010
%E Changed offset to 1 by _Michael Somos_, Sep 17 2018
