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 A054660 Number of monic irreducible polynomials over GF(4) with fixed nonzero trace. 10
 1, 2, 5, 16, 51, 170, 585, 2048, 7280, 26214, 95325, 349520, 1290555, 4793490, 17895679, 67108864, 252645135, 954437120, 3616814565, 13743895344, 52357696365, 199911205050, 764877654105, 2932031006720, 11258999068416 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also number of Lyndon words of length n with trace 1 over GF(4). Let x = RootOf( z^2+z+1 ) and y = 1+x. Also number of Lyndon words of length n with trace x over GF(4). Also number of Lyndon words of length n with trace y over GF(4). LINKS Seiichi Manyama, Table of n, a(n) for n = 1..1000 FORMULA From Seiichi Manyama, Mar 11 2018: (Start) a(n) = A000048(2*n) = (1/(4*n)) * Sum_{odd d divides n} mu(d)*4^(n/d), where mu is the Möbius function A008683. a(n+1) = A300628(n,n) for n >= 0. (End) EXAMPLE a(3; y)=5 since the five 4-ary Lyndon words of trace y and length 3 are { 00y, 01x, 0x1, 11y, xxy }. CROSSREFS Cf. A000048, A051841, A046211, A046209, A054661, etc. Cf. A008683, A054661, A074025, A300628. Sequence in context: A148386 A148387 A121651 * A231296 A148388 A148389 Adjacent sequences:  A054657 A054658 A054659 * A054661 A054662 A054663 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Apr 18 2000 EXTENSIONS More terms from James A. Sellers, Apr 19 2000 STATUS approved

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Last modified October 27 15:27 EDT 2020. Contains 338035 sequences. (Running on oeis4.)