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 A038519 Number of elements of GF(2^n) with trace 0 and subtrace 1. 4
 1, 0, 1, 3, 2, 10, 16, 28, 72, 120, 256, 528, 992, 2080, 4096, 8128, 16512, 32640, 65536, 131328, 261632, 524800, 1048576, 2096128, 4196352, 8386560, 16777216, 33558528, 67100672, 134225920, 268435456, 536854528, 1073774592 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 F. Ruskey, Number of irreducible polynomials over GF(2) with given trace and subtrace F. Ruskey, Number of elements of GF(2^n) with given trace and subtrace Index entries for linear recurrences with constant coefficients, signature (0,2,4). FORMULA a(n) = C(n, r+0) + C(n, r+4) + C(n, r+8) + ... where r = 2 if n odd, r = 0 if n even. From Colin Barker, Aug 02 2019: (Start) G.f.: (1 - x^2 - x^3) / ((1 - 2*x)*(1 + 2*x + 2*x^2)). - Creighton Dement, Apr 29 2005, corrected by Colin Barker, Aug 02 2019 a(n) = ((-1-i)^n + (-1+i)^n + 2^n) / 4 for n>0. a(n) = 2*a(n-2) + 4*a(n-3) for n>3. (End) PROG (PARI) Vec((1 - x^2 - x^3) / ((1 - 2*x)*(1 + 2*x + 2*x^2)) + O(x^40)) \\ Colin Barker, Aug 02 2019 (Magma) I:=[1, 0, 1, 3]; [m le 4 select I[m] else 2*Self(m-2)+4*Self(m-3):m in [1..33]]; // Marius A. Burtea, Aug 02 2019 CROSSREFS Cf. A038503, A038505, A038518, A038520, A038521. Sequence in context: A025520 A099946 A011953 * A192617 A082219 A034461 Adjacent sequences: A038516 A038517 A038518 * A038520 A038521 A038522 KEYWORD easy,nonn AUTHOR Frank Ruskey STATUS approved

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Last modified December 8 13:46 EST 2023. Contains 367679 sequences. (Running on oeis4.)