A305494 Let s(D) = Sum_{(a,b,c)} j((-b+sqrt(D))/(2*a)) where (a,b,c) is taken over all the primitive reduced binary quadratic forms a*x^2+b*xy+c*y^2 with b^2-4*ac = D. This sequence is s(D) as D runs through the numbers -3, -4, -7, -8, -11, -12, ... .

0, 1728, -3375, 8000, -32768, 54000, -191025, 287496, -884736, 1264000, -3491750, 4834944, -12288000, 16581375, -39491307, 52250000, -117964800, 153542016, -331531596, 425692800, -884736000, 1122662608, -2257834125, 2835810000, -5541101568, 6896880000, -13136684625

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..1000

Example

In the case D = -15,
j((1+sqrt(-15))/2) + j((1+sqrt(-15))/4) = (-191025-85995*sqrt(5))/2 + (-191025+85995*sqrt(5))/2 = -191025.
  ----+-------------------------------------------+---------
    D | Coefficients of Hilbert class polynomial  |   a(n)
  ----+-------------------------------------------+---------
   -3 |              0,            1;             |        0
   -4 |          -1728,            1;             |     1728
   -7 |           3375,            1;             |    -3375
   -8 |          -8000,            1;             |     8000
  -11 |          32768,            1;             |   -32768
  -12 |         -54000,            1;             |    54000
  -15 |     -121287375,       191025,        1;   |  -191025
  -16 |        -287496,            1;             |   287496
  -19 |         884736,            1;             |  -884736
  -20 |     -681472000,     -1264000,        1;   |  1264000
  -23 | 12771880859375,  -5151296875,  3491750, 1;| -3491750
  -24 |    14670139392,     -4834944,        1;   |  4834944

Crossrefs

Cf. A014601, A032354, A305474.

Sequence in context: A280841 A305474 A302142 * A032354 A305475 A202458

Adjacent sequences: A305491 A305492 A305493 * A305495 A305496 A305497

Keyword

sign

Author

Seiichi Manyama, Jun 02 2018

Status

approved