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 A028941 #32 Dec 26 2024 15:46:58
%S A028941 1,1,1,1,4,1,9,25,49,16,529,841,3481,16641,98596,4225,2337841,
%T A028941 13608721,67387681,264517696,6941055969,12925188721,384768368209,
%U A028941 5677664356225,61935294530404,49020596163841,16063784753682169
%N A028941 Denominator of X-coordinate of n*P where P is the generator [0,0] for rational points on curve y^2+y = x^3-x.
%C A028941 We can take P = P[1] = [x_1, y_1] = [0,0]. Then P[n] = P[1]+P[n-1] = [x_n, y_n] for n >= 2. Sequence gives denominators of the x_n. - _N. J. A. Sloane_, Jan 27 2022
%C A028941 Squares of terms in A006769 (or A006720).
%D A028941 G. Everest, A. J. van der Poorten, I. Shparlinski and T. Ward, Recurrence Sequences: Examples and Applications, AMS Monographs, 2003
%D A028941 A. W. Knapp, Elliptic Curves, Princeton 1992, p. 77.
%H A028941 Seiichi Manyama, <a href="/A028941/b028941.txt">Table of n, a(n) for n = 1..212</a>
%H A028941 B. Mazur, <a href="https://doi.org/10.1090/S0273-0979-1986-15430-3">Arithmetic on curves</a>, Bull. Amer. Math. Soc. 14 (1986), 207-259; see p. 225.
%F A028941 This sequence satisfies the quadratic recurrence relation a(n)a(n-6)=-a(n-1)a(n-5)+2a(n-2)a(n-4)+2a(n-3)^2 which is a generalized Somos-6 relation. - Graham Everest (g.everest(AT)uea.ac.uk), Dec 16 2002
%F A028941 P=(0, 0), 2P=(1, 0), if kP=(a, b) then (k+1)P=(a'=(b^2-a^3)/a^2, b'=-1-b*a'/a).
%t A028941 nxt[{a_,b_,c_,d_,e_,f_}]:={b,c,d,e,f,((c*2e)-f*b+2d^2)/a}; NestList[nxt,{1,1,1,1,4,1},30][[;;,1]] (* _Harvey P. Dale_, Dec 26 2024 *)
%o A028941 (PARI) - see A028940.
%Y A028941 Cf. A028940, A028942, A028943.
%K A028941 nonn,frac
%O A028941 1,5
%A A028941 _N. J. A. Sloane_