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Search: id:A054660
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| A054660 |
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Number of monic irreducible polynomials over GF(4) with fixed nonzero trace. |
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+0
7
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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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).
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LINKS
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F. Ruskey, Number of monic irreducible polynomials over GF(q) with zero trace ...
F. Ruskey, Number of Lyndon words of given trace
F. Ruskey, Number of Lyndon words over GF(q) of given trace.
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EXAMPLE
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a(3; y)=5 since the five 4-ary Lyndon words of trace y and length 3 are { 00y, 01x, 0x1, 11y, xxy }.
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CROSSREFS
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Cf. A000048, A051841, A046211, A046209, A054661, etc.
Cf. A054661, A074025.
Sequence in context: A148386 A148387 A121651 this_sequence A148388 A148389 A108529
Adjacent sequences: A054657 A054658 A054659 this_sequence A054661 A054662 A054663
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Apr 18 2000
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Apr 19 2000
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