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A213243
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Number of nonzero elements in GF(2^n) that are cubes.
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11
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1, 1, 7, 5, 31, 21, 127, 85, 511, 341, 2047, 1365, 8191, 5461, 32767, 21845, 131071, 87381, 524287, 349525, 2097151, 1398101, 8388607, 5592405, 33554431, 22369621, 134217727, 89478485, 536870911, 357913941, 2147483647, 1431655765, 8589934591, 5726623061, 34359738367, 22906492245
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OFFSET
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1,3
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LINKS
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FORMULA
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a(n) = M / gcd( M, 3 ), where M=2^n-1.
a(n) = (-1)*((-2+(-1)^n)*(-1+2^n))/3.
a(n) = 5*a(n-2) - 4*a(n-4).
G.f.: x*(2*x^2+x+1) / ((x-1)*(x+1)*(2*x-1)*(2*x+1)). (End)
E.g.f.: (-1 + exp(x) - 2*exp(3*x) + 2*exp(4*x))*exp(-2*x)/3. - Ilya Gutkovskiy, Apr 22 2016
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MAPLE
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MATHEMATICA
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LinearRecurrence[{0, 5, 0, -4}, {1, 1, 7, 5}, 40] (* Harvey P. Dale, Jan 05 2017 *)
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PROG
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(Magma) [(2^n - 1) / GCD (2^n - 1, 3): n in [1..40]]; // Vincenzo Librandi, Mar 16 2013
(PARI) a(n)=(2^n-1)/gcd(2^n-1, 3) \\ Edward Jiang, Sep 04 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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