A371193 a(n) = 2^(4*n-4)*(2^n-1).

0, 1, 48, 1792, 61440, 2031616, 66060288, 2130706432, 68451041280, 2194728288256, 70300024700928, 2250700302057472, 72040001851883520, 2305561534236983296, 73782472695210835968, 2361111183840784678912, 75556710804409716572160, 2417833192485184639860736

Offset

0,3

Comments

It appears that 16*a(n) (that is, the sequence 16, 768, 28672, 983040, 32505856, 1056964608, 34091302912, ...) is the number of nonsingular generalized Weierstrass curves over GF(2^n), n>0.

Links

Table of n, a(n) for n=0..17.

Param Parekh, Paavan Parekh, Sourav Deb, and Manish K. Gupta, On the Classification of Weierstrass Elliptic Curves over Z_n, arXiv:2310.11768 [cs.CR], 2023. See Table 1.

Index entries for linear recurrences with constant coefficients, signature (48,-512).

Formula

From Chai Wah Wu, Nov 18 2025: (Start)

a(n) = 48*a(n-1) - 512*a(n-2) for n > 1.

G.f.: x/((16*x - 1)*(32*x - 1)). (End)

Mathematica

Table[2^(4n-4) (2^n-1), {n, 0, 20}] (* or *) LinearRecurrence[{48, -512}, {0, 1}, 20] (* Harvey P. Dale, Nov 29 2025 *)

Prog

(Python)
def A371193(n): return (1<<n)-1<<(n-1<<2) if n else 0 # Chai Wah Wu, Mar 14 2024
(PARI) a(n)=(32^n-16^n)/16 \\ Charles R Greathouse IV, May 31 2026

Crossrefs

Equals A163839 divided by 4.

Cf. A371195.

Sequence in context: A273627 A355998 A288455 * A231450 A152068 A290404

Adjacent sequences: A371190 A371191 A371192 * A371194 A371195 A371196

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 14 2024

Status

approved