This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A178079 #31 Jan 05 2025 19:51:39
%S A178079 0,1,1,1,2,1,-3,-7,-8,-25,-37,47,318,559,2023,7039,-496,-90431,
%T A178079 -314775,-1139599,-8007614,-13512079,154788437,1247862041,5097732072,
%U A178079 56844671623,290379801907,-1403230649825,-32188159859842,-199066111517153
%N A178079 A (1,-1) Somos-4 sequence.
%C A178079 Hankel transform of A178078 is a(n+2).
%C A178079 Apparently a(n) = -A174400(n+1). - _R. J. Mathar_, Dec 10 2010
%C A178079 This is a strong elliptic divisibility sequence t_n as given in [Kimberling, p. 16] where x = 1, y = 1, z = 2. - _Michael Somos_, Aug 06 2014
%C A178079 Associated with elliptic curve "61a1" y^2 + x*y = x^3 - 2*x + 1 and point (1, -1). - _Michael Somos_, Sep 27 2018
%H A178079 G. C. Greubel, <a href="/A178079/b178079.txt">Table of n, a(n) for n = 0..150</a>
%H A178079 Paul Barry, <a href="https://arxiv.org/abs/2306.05025">Integer sequences from elliptic curves</a>, arXiv:2306.05025 [math.NT], 2023.
%H A178079 Clark Kimberling, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/17-1/kimberling1.pdf">Strong divisibility sequences and some conjectures</a>, Fib. Quart., 17 (1979), 13-17.
%H A178079 LMFDB, <a href="http://www.lmfdb.org/EllipticCurve/Q/61/a/1">Elliptic Curve 61.a1 (Cremona label 61a1)</a>
%F A178079 a(n) = (a(n-1)*a(n-3) - a(n-2)^2)/a(n-4), n>=4.
%F A178079 a(n) = -a(-n) for all n in Z. - _Michael Somos_, Aug 06 2014
%F A178079 0 = 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 27 2018
%t A178079 Join[{0}, RecurrenceTable[{a[n] == (a[n - 1]*a[n - 3] - a[n - 2]^2)/a[n - 4], a[1] == 1, a[2] == 1, a[3] == 1, a[4] == 2}, a, {n, 1, 50}]] (* _G. C. Greubel_, Sep 22 2018 *)
%t A178079 nxt[{a_,b_,c_,d_}]:={b,c,d,(d*b-c^2)/a}; Join[{0},NestList[nxt,{1,1,1,2},30][[;;,1]]] (* _Harvey P. Dale_, Sep 27 2023 *)
%o A178079 (Magma) I:=[0,1,1,1,2]; [n le 5 select I[n] else (Self(n-1)*Self(n-3)-Self(n-2)^2)/Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Aug 07 2014
%o A178079 (PARI) m=50; v=concat([1,1,1,2], vector(m-4)); for(n=5, m, v[n] = (v[n-1]*v[n-3] - v[n-2]^2)/v[n-4]); concat([0], v) \\ _G. C. Greubel_, Sep 22 2018
%o A178079 (PARI) {a(n) = my(E = ellinit([1, 0, 0, -2, 1]), z = ellpointtoz(E, [1, -1])); round( ellsigma(E, n*z) / ellsigma(E, z)^n^2)}; /* _Michael Somos_, Sep 27 2018 */
%K A178079 easy,sign
%O A178079 0,5
%A A178079 _Paul Barry_, May 19 2010
%E A178079 Missing a(0)=0 and a(1)=1 added by _Michael Somos_, Aug 06 2014
%E A178079 More terms from _Vincenzo Librandi_, Aug 07 2014