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

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

1,3

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.

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

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 }.

Crossrefs

Cf. A074446, A074447, A074448, A074450.

Cf. A054660, A073995, A073996, A073997, A073998, A073999.

Sequence in context: A131529 A238111 A165901 * A364622 A359328 A332235

Adjacent sequences: A074446 A074447 A074448 * A074450 A074451 A074452

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