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A259191 Number of integral solutions to y^2 = x^3 + n*x^2 + n (with y nonnegative). 1
3, 0, 0, 4, 1, 0, 0, 0, 2, 0, 0, 1, 1, 0, 0, 3, 1, 0, 0, 0, 0, 0, 0, 1, 8, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 6, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 6, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

If n is square there are at least two solutions, corresponding to x = 0 and x = -n. If n = 2^(2k) there are at least three solutions, corresponding to x = 0, x = -2^(2k), and x = 2^(6k-2) + 2^(2k). If n = 2k^2 + 2k, there is at least one solution, corresponding to x = 1.

LINKS

Table of n, a(n) for n=1..82.

PROG

(Sage)

for i in range(1, 31):

    E=EllipticCurve([0, i, 0, 0, i])

    print(len(E.integral_points()))

CROSSREFS

Cf. A081119, A081120.

Sequence in context: A133109 A130208 A288654 * A240455 A304263 A305223

Adjacent sequences:  A259188 A259189 A259190 * A259192 A259193 A259194

KEYWORD

nonn

AUTHOR

Morris Neene, Jun 20 2015

STATUS

approved

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Last modified August 10 11:12 EDT 2020. Contains 336379 sequences. (Running on oeis4.)