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

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 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

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

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