A213243 Number of nonzero elements in GF(2^n) that are cubes.
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
Offset: 1
Keywords
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (0,5,0,-4).
Crossrefs
Programs
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Magma
[(2^n - 1) / GCD (2^n - 1, 3): n in [1..40]]; // Vincenzo Librandi, Mar 16 2013
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Maple
A213243:=n->(2^n-1)/gcd(2^n-1,3): seq(A213243(n), n=1..50); # Wesley Ivan Hurt, Aug 23 2014
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Mathematica
Table[(2^n - 1)/GCD[2^n - 1, 3], {n, 50}] (* Vincenzo Librandi, Mar 16 2013 *) LinearRecurrence[{0,5,0,-4},{1,1,7,5},40] (* Harvey P. Dale, Jan 05 2017 *) -
PARI
a(n)=(2^n-1)/gcd(2^n-1,3) \\ Edward Jiang, Sep 04 2014
Formula
a(n) = M / gcd( M, 3 ), where M=2^n-1.
Conjectures from Colin Barker, Aug 23 2014, verified by Robert Israel, Apr 22 2016: (Start)
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