A305594 Number of cyclic binary sequences of length n containing no abelian 4th powers.

2, 3, 4, 4, 4, 8, 10, 14, 12, 20, 34, 33, 52, 61, 76, 96, 126, 200, 258, 442, 568, 889, 1224, 1264, 1020, 1697, 2394, 3672, 4500, 9257, 9442, 7218, 9654, 9596, 11040, 12698, 16152, 21937, 31662, 25564, 29106, 30530, 43820, 50383, 66108, 75166, 100160, 117416, 129892

Offset

1,1

Comments

Two length-n sequences are considered to be the same in the cyclic sense if one is a cyclic shift of the other.

An abelian 4th power is a word of the form x x' x'' x''', where x', x'', x''' are all permutations of x.

Links

Bert Dobbelaere, Table of n, a(n) for n = 1..70

Example

a(7) = 10, and the cyclic words are {0001001, 0001011, 0001101, 0010011, 0010101, 0010111, 0011011, 0011101, 0101011, 0110111}.

Crossrefs

Sequence in context: A309941 A352457 A211509 * A320778 A353948 A334049

Adjacent sequences: A305591 A305592 A305593 * A305595 A305596 A305597

Keyword

nonn

Author

Jeffrey Shallit, Jun 05 2018

Extensions

More terms from Bert Dobbelaere, Nov 16 2025

Status

approved