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.

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A074413 Number of 4-ary Lyndon words of length n over Z_4 with trace 2 and subtrace 3.

Original entry on oeis.org

0, 0, 2, 6, 16, 44, 128, 440, 1706, 6496, 24576, 90004, 327680, 1198336, 4438966, 16645120, 62914560, 238602228, 905969664, 3442672434, 13102206738, 49977802752, 191126044672, 732649663000, 2814062572336, 10825959342080, 41705086880768, 160862475536676
Offset: 1

Views

Author

Frank Ruskey and Nate Kube, Aug 22 2002

Keywords

Examples

			a(4;2,3)=6 since the six 4-ary Lyndon words of trace 2, subtrace 3 and length 4 are { 0123, 0132, 0213, 0231, 0312, 0321 }.

Links

Crossrefs

Cf. A068596, A074403, A074404, A074405, A074406, A074407, A074408, A074409, A074410, A074411, A074412.

Extensions

Terms a(15) onward from Max Alekseyev, Apr 09 2013

A054664 Number of 4-ary Lyndon words of length n with trace 0 mod 4.

Original entry on oeis.org

1, 1, 5, 14, 51, 165, 585, 2032, 7280, 26163, 95325, 349350, 1290555, 4792905, 17895679, 67106816, 252645135, 954429840, 3616814565, 13743869130, 52357696365, 199911109725, 764877654105, 2932030657200, 11258999068416
Offset: 1

Views

Author

N. J. A. Sloane, Apr 18 2000

Keywords

Comments

Also number of 4-ary Lyndon words of length n with trace 2 mod 4.

Links

Crossrefs

Cf. A000048, A051841, A046211, A046209, A054660, etc.

Programs

  • Mathematica
    a[n_] := 1/(4 n) Sum[GCD[d, 4] MoebiusMu[d] 4^(n/d), {d, Divisors[n]}];
Array[a, 30] (* Andrey Zabolotskiy, Dec 19 2020 *)

Formula

From Andrey Zabolotskiy, Dec 19 2020: (Start)
a(n) = A068596(n) + A074403(n) + A074404(n) + A074405(n).
a(n) = A074410(n) + A074411(n) + A074412(n) + A074413(n). (End)

Extensions

More terms from James Sellers, Apr 19 2000
Previous Showing 11-12 of 12 results.

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

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