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 A038521 Number of elements of GF(2^n) with trace 1 and subtrace 1. 5
 0, 2, 1, 4, 10, 12, 36, 64, 120, 272, 496, 1024, 2080, 4032, 8256, 16384, 32640, 65792, 130816, 262144, 524800, 1047552, 2098176, 4194304, 8386560, 16781312, 33550336, 67108864, 134225920, 268419072, 536887296, 1073741824, 2147450880 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 K. Cattel, C. R. Miers, F. Ruskey, J. Sawada, M. Serra, The number of irreducible polynomials over Gf(2) with given trace and subtrace, J. Combin. Math. Combin. Comput. 47 (2003) 31-64. [From R. J. Mathar, Oct 20 2008] 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 = 3 if n odd, r = 1 if n even. From Colin Barker, Aug 02 2019: (Start) G.f.: x*(2 + x) / ((1 - 2*x)*(1 + 2*x + 2*x^2)). a(n) = ((-1-i)^(-1+n) + (-1+i)^(-1+n) + 2^n) / 2. a(n) = 2*a(n-2) + 4*a(n-3) for n>2. (End) MAPLE A038521 := proc(n) local r, a, i ; if n mod 2 = 1 then r := 3 ; else r := 1 ; fi; a :=0 ; for i from r to n by 4 do a := a+binomial(n, i) ; od; a ; end: for n from 1 to 40 do printf("%d, ", A038521(n)) ; od: # R. J. Mathar, Oct 20 2008 MATHEMATICA LinearRecurrence[{0, 2, 4}, {0, 2, 1}, 33] (* Jean-François Alcover, May 08 2023 *) PROG (PARI) concat(0, Vec(x*(2 + x) / ((1 - 2*x)*(1 + 2*x + 2*x^2)) + O(x^35))) \\ Colin Barker, Aug 02 2019 (Magma) I:=[0, 2, 1]; [m le 3 select I[m] else 2*Self(m-2) + 4*Self(m-3): m in [1..33]] // Marius A. Burtea, Aug 02 2019 CROSSREFS Cf. A038504, A000749. Cf. A038518, A038519, A038520. Cf. A134654. - R. J. Mathar, Oct 20 2008 Sequence in context: A212770 A205855 A329709 * A134654 A198262 A085421 Adjacent sequences: A038518 A038519 A038520 * A038522 A038523 A038524 KEYWORD easy,nonn AUTHOR Frank Ruskey EXTENSIONS Values duplicated A038520 and were replaced by R. J. Mathar, Oct 20 2008 STATUS approved

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Last modified December 8 14:49 EST 2023. Contains 367680 sequences. (Running on oeis4.)