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

Author

Frank Ruskey and Nate Kube, Aug 23 2002

Keywords

• nonn

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

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

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