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A169877
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Maximum number of rational points on a smooth absolutely irreducible projective curve of genus 1 over the field F_3^n.
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1
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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
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OFFSET
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1,1
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LINKS
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FORMULA
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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
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PROG
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(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:
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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