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A334068 Negative of numerator of y-coordinate of -(2n+1)*P where P is the generator for rational points on the curve y^2 + y = x^3 - x.

%I A334068 #10 Oct 06 2020 14:42:52
%S A334068 1,0,3,35,-92,8555,162024,2882165,3906507129,-88075171080,
%T A334068 260151768440137,304986999070045520,-100886180199254542253,
%U A334068 1600059682932627475385835,2620000542207768964443625516
%N A334068 Negative of numerator of y-coordinate of -(2n+1)*P where P is the generator for rational points on the curve y^2 + y = x^3 - x.
%H A334068 Robert Israel, <a href="/A334068/b334068.txt">Table of n, a(n) for n = 0..86</a>
%F A334068 a(n) = A028934(-1-n) = A028942(-2*n-1) for all n in Z.
%F A334068 0 = a(n)*a(n+8) -145*a(n+1)*a(n+7) +3225*a(n+2)*a(n+6) -18705*a(n+3)*a(n+5) +14964*a(n+4)*a(n+4) for all n in Z.
%e A334068 -P = (0, -1), -3P = (-1 ,0), -5P = (1/4, -3/8), -7P = (-5/9, -35/27).
%p A334068 f:= proc(m) option remember; -(-145*procname(m - 7)*procname(m - 1) + 3225*procname(m - 6)*procname(m - 2) - 18705*procname(m - 5)*procname(m - 3) + 14964*procname(m - 4)^2)/procname(m - 8) end proc:
%p A334068 Data:= [1, 0, 3, 35, -92, 8555, 162024, 2882165, 3906507129, -88075171080]:
%p A334068 for i from 0 to 9 do f(i):= Data[i+1] od:
%p A334068 map(f, [$0..20]); # _Robert Israel_, Oct 06 2020
%o A334068 (PARI) {a(n) = -numerator(ellmul(ellinit([0, 0, 1, -1, 0]), [0, 0], -2*n-1)[2])};
%Y A334068 Cf. A028934, A028942.
%K A334068 sign
%O A334068 0,3
%A A334068 _Michael Somos_, Apr 13 2020