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 A213243 Number of nonzero elements in GF(2^n) that are cubes. 10
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 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). 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 MAPLE A213243:=n->(2^n-1)/gcd(2^n-1, 3): seq(A213243(n), n=1..50); # Wesley Ivan Hurt, Aug 23 2014 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 *) PROG (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 CROSSREFS Cf. A213244 (5th powers), A213245 (7th powers), A213246 (9th powers), A213247 (11th powers), A213248 (13th powers). Sequence in context: A146619 A059990 A213246 * A185269 A070426 A142883 Adjacent sequences:  A213240 A213241 A213242 * A213244 A213245 A213246 KEYWORD nonn AUTHOR Joerg Arndt, Jun 07 2012 STATUS approved

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