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A336398
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Number of rational knots (or two-bridge knots) with n crossings (chiral pairs counted as distinct).
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4
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0, 2, 1, 4, 5, 14, 21, 48, 85, 182, 341, 704, 1365, 2774, 5461, 11008, 21845, 43862, 87381, 175104, 349525, 699734, 1398101, 2797568, 5592405, 11187542, 22369621, 44744704, 89478485, 178967894, 357913941, 715849728
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OFFSET
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2,2
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LINKS
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FORMULA
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(2^(n-2) - 1) / 3 if n is even,
(2^(n-2) + 2^((n-1)/2)) / 3 if n = 1 (mod 4),
(2^(n-2) + 2^((n-1)/2) + 2) / 3 if n = 3 (mod 4).
a(n) = a(n-1) + 3*a(n-2) - a(n-3) - 2*a(n-5) - 4*a(n-6).
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PROG
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(Python) [(2**(n-2) + [-1, 2**(n//2), -1, 2**(n//2)+2][n%4])//3 for n in range(2, 30)]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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