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.

1, 0, 3, 35, -92, 8555, 162024, 2882165, 3906507129, -88075171080, 260151768440137, 304986999070045520, -100886180199254542253, 1600059682932627475385835, 2620000542207768964443625516

Offset: 0

Author

Michael Somos, Apr 13 2020

Keywords

• sign

Examples

			-P = (0, -1), -3P = (-1 ,0), -5P = (1/4, -3/8), -7P = (-5/9, -35/27).
		

Links

• Robert Israel, Table of n, a(n) for n = 0..86

Crossrefs

Cf. A028934, A028942.

Programs

Maple

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:
Data:= [1, 0, 3, 35, -92, 8555, 162024, 2882165, 3906507129, -88075171080]:
for i from 0 to 9 do f(i):= Data[i+1] od:
map(f, [$0..20]); # Robert Israel, Oct 06 2020

PARI

{a(n) = -numerator(ellmul(ellinit([0, 0, 1, -1, 0]), [0, 0], -2*n-1)[2])};

Formula

a(n) = A028934(-1-n) = A028942(-2*n-1) for all n in Z.

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.