cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A054661 Number of monic irreducible polynomials over GF(4) with zero trace.

Original entry on oeis.org

1, 0, 5, 12, 51, 160, 585, 2016, 7280, 26112, 95325, 349180, 1290555, 4792320, 17895679, 67104768, 252645135, 954422560, 3616814565, 13743842916, 52357696365, 199911014400, 764877654105, 2932030307680, 11258999068416
Offset: 1

Views

Author

N. J. A. Sloane, Apr 18 2000

Keywords

Comments

Also number of Lyndon words of length n with trace 0 over GF(4).

Links

Crossrefs

Cf. A000048, A051841, A046211, A046209, A054660, A074031, A074032, A074446, A074447.

Formula

From Andrey Zabolotskiy, Dec 17 2020: (Start)
a(n) = A074031(n) + 3 * A074032(n).
a(n) = A074446(n) + 3 * A074447(n). (End)

Extensions

More terms from James Sellers, Apr 19 2000

A074450 Let x = RootOf(z^2 + z + 1) and y = 1+x. Number of 4-ary Lyndon words of length n over GF(4) with trace 1 and subtrace x.

Original entry on oeis.org

0, 0, 1, 4, 12, 40, 144, 512, 1813, 6528, 23808, 87380, 322560, 1198080, 4473647, 16777216, 63160320, 238605640, 904200192, 3435973836, 13089411609, 49977753600, 191219367936, 733007751680, 2814749599332, 10825959997440, 41699995927744, 160842843834660, 621186153185280
Offset: 1

Views

Author

Frank Ruskey and Nate Kube, Aug 23 2002

Keywords

Comments

Also the number of 4-ary Lyndon words of length n over GF(4) with trace 1 and subtrace y. Also the number of 4-ary Lyndon words of length n over GF(4) with trace x and subtrace 1. Also the number of 4-ary Lyndon words of length n over GF(4) with trace x and subtrace x. Also the number of 4-ary Lyndon words of length n over GF(4) with trace y and subtrace 1. Also the number of 4-ary Lyndon words of length n over GF(4) with trace y and subtrace y.
Is this a duplicate of A074032? - R. J. Mathar, Dec 15 2020

Links

Crossrefs

Cf. A074446, A074447, A074448, A074449.
Cf. A054660, A073995, A073996, A073997, A073998, A073999.

Extensions

Terms a(16) and beyond from Andrey Zabolotskiy, Jul 21 2021

A074447 Number of 4-ary Lyndon words of length n over GF(4) with trace 0 and subtrace 1.

Original entry on oeis.org

0, 0, 1, 2, 12, 40, 144, 496, 1813, 6528, 23808, 87210, 322560, 1198080, 4473647, 16775168, 63160320, 238605640, 904200192, 3435947622, 13089411609, 49977753600, 191219367936, 733007402160, 2814749599332, 10825959997440, 41699995927744, 160842839041170, 621186153185280
Offset: 1

Views

Author

Frank Ruskey and Nate Kube, Aug 23 2002

Keywords

Comments

Let x = RootOf( z^2+z+1 ) and y = 1+x. Also the number of 4-ary Lyndon words of length n over GF(4) with trace 0 and subtrace x. Also the number of 4-ary Lyndon words of length n over GF(4) with trace 0 and subtrace y.

Examples

			a(4;0,1)=2 since the two 4-ary Lyndon words of trace 0, subtrace 1 and length 4 are { 0011, 11xx }, where x = RootOf( z^2+z+1 ).

Links

Crossrefs

Cf. A074446, A074448, A074449, A074450.
Cf. A054661, A073995, A073996, A073997, A073998, A073999.

Extensions

Terms a(16) and beyond from Andrey Zabolotskiy, Jul 21 2021

A074448 Number of 4-ary Lyndon words of length n over GF(4) with trace 1 and subtrace 0.

Original entry on oeis.org

1, 1, 1, 4, 15, 45, 144, 512, 1841, 6579, 23808, 87380, 322875, 1198665, 4473647, 16777216, 63164175, 238612920, 904200192, 3435973836, 13089461538, 49977848925, 191219367936, 733007751680, 2814750270420, 10825961287995, 41699995927744, 160842843834660, 621186162441675
Offset: 1

Views

Author

Frank Ruskey and Nate Kube, Aug 23 2002

Keywords

Comments

Let x = RootOf(z^2 + z + 1) and y = 1 + x. Also the number of 4-ary Lyndon words of length n over GF(4) with trace x and subtrace 0. Also the number of 4-ary Lyndon words of length n over GF(4) with trace y and subtrace 0.

Links

Crossrefs

Cf. A074446, A074447, A074449, A074450.
Cf. A054660, A073995, A073996, A073997, A073998, A073999.

Extensions

Terms a(16) and beyond from Andrey Zabolotskiy, Jul 21 2021

A074449 Number of 4-ary Lyndon words of length n over GF(4) with trace 1 and subtrace 1.

Original entry on oeis.org

0, 1, 2, 4, 12, 45, 153, 512, 1813, 6579, 23901, 87380, 322560, 1198665, 4474738, 16777216, 63160320, 238612920, 904213989, 3435973836, 13089411609, 49977848925, 191219550297, 733007751680, 2814749599332, 10825961287995, 41699998413248, 160842843834660, 621186153185280
Offset: 1

Views

Author

Frank Ruskey and Nate Kube, Aug 23 2002

Keywords

Comments

Let x = RootOf( z^2+z+1 ) and y = 1+x. Also the number of 4-ary Lyndon words of length n over GF(4) with trace x and subtrace y. Also the number of 4-ary Lyndon words of length n over GF(4) with trace y and subtrace x.

Examples

			Let x = RootOf( z^2+z+1 ) and y = 1+x. a(2; y,x)=1 since the one 4-ary Lyndon word of trace y, subtrace x and length 2 is { 1x }.

Links

Crossrefs

Cf. A074446, A074447, A074448, A074450.
Cf. A054660, A073995, A073996, A073997, A073998, A073999.

Extensions

Terms a(16) and beyond from Andrey Zabolotskiy, Jul 21 2021
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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