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

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

1,4

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.

Links

Table of n, a(n) for n=1..29.

F. Ruskey, 4-ary Lyndon words with given trace and subtrace over GF(4)

Example

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 ).

Crossrefs

Cf. A074446, A074448, A074449, A074450.

Cf. A054661, A073995, A073996, A073997, A073998, A073999.

Sequence in context: A069144 A013194 A212874 * A190064 A240122 A110953

Adjacent sequences: A074444 A074445 A074446 * A074448 A074449 A074450

Keyword

nonn

Author

Frank Ruskey and Nate Kube, Aug 23 2002

Extensions

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

Status

approved