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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.
Adjacent sequences: A054657 A054658 A054659 this_sequence A054661 A054662 A054663
Sequence in context: A005497 A118973 A121651 this_sequence A108529 A011819 A001428
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KEYWORD
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nonn,easy
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AUTHOR
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njas, 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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