A362374 Number of solutions of y^2 + y = x^3 + x where x and y are in GF(2^n).

4, 4, 4, 24, 24, 64, 144, 224, 544, 1024, 1984, 4224, 8064, 16384, 33024, 65024, 131584, 262144, 523264, 1050624, 2095104, 4194304, 8392704, 16769024, 33562624, 67108864, 134201344, 268468224, 536838144, 1073741824, 2147549184, 4294836224, 8590065664

Offset: 1

Author

Michel Marcus, Apr 20 2023

Keywords

• nonn
• easy

Links

• Paolo Xausa, Table of n, a(n) for n = 1..1000
• John C. Baez, Motivating Motives, arXiv:2304.08737 [math.NT], 2023. See pp. 4-5.
• Index entries for linear recurrences with constant coefficients, signature (0,2,4).

Crossrefs

Cf. A038518.

Programs

Mathematica

LinearRecurrence[{0, 2, 4}, {4, 4, 4}, 50] (* Paolo Xausa, May 28 2024 *)

Formula

a(n) = 4 * A038518(n). - Joerg Arndt, Apr 20 2023

From Stefano Spezia, May 28 2024: (Start)

G.f.: 4*x*(1 + x - x^2)/((1 - 2*x)*(1 + 2*x + 2*x^2)).

E.g.f.: 2*cosh(x)*(cosh(x) - cos(x)) + 2*(cosh(x) + cos(x))*sinh(x). (End)