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A169877 Maximum number of rational points on a smooth absolutely irreducible projective curve of genus 1 over the field F_3^n. 1
7, 16, 38, 100, 275, 784, 2280, 6724, 19964, 59536, 177989, 532900, 1596849, 4787344, 14356482, 43059844, 129162891, 387459856, 1162329651, 3486902500, 10460557755, 31381413904, 94143792483, 282430599364, 847290450408, 2541869016976, 7625603007884, 22876802020900, 68630393933574 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Max Deuring, Die Typen der Multiplikatorenringe elliptischer Funktionenkörper, Abh. Math. Sem. Hansischen Univ. 14 (1941), 197-272.
Gerard van der Geer et al., Tables of curves with many points
Gerard van der Geer and Marcel van der Vlugt, Tables of curves with many points, Math. Comp. 69 (2000) 797-810.
W. C. Waterhouse, Abelian varieties over finite fields, Ann Sci. E.N.S., (4) 2 (1969), 521-560.
FORMULA
a(n) = 3^n + 1 + floor(2*3^(n/2)) if 3 does not divide floor(2*3^(n/2)), n is even, or n = 1. Otherwise a(n) = 3^n + floor(2*3^(n/2)) [Deuring-Waterhouse]. - Robin Visser, Aug 17 2023
PROG
(Sage)
def a(n):
if (n==1) or (n%2 == 0) or (floor(2*3^(n/2))%3 != 0):
return 3^n + 1 + floor(2*3^(n/2))
else:
return 3^n + floor(2*3^(n/2)) # Robin Visser, Aug 17 2023
CROSSREFS
Sequence in context: A176449 A278945 A327628 * A286710 A036834 A020941
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jul 05 2010
EXTENSIONS
More terms from Robin Visser, Aug 17 2023
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)