A118311 Number of dissimilar squarefree quaternary words of length n.

1, 1, 2, 4, 11, 29, 77, 202, 532, 1395, 3664, 9605, 25192, 66047, 173183, 453998, 1190259, 3120294, 8180124, 21444290, 56217025, 147373441, 386342414, 1012799936, 2655067412, 6960281083, 18246444362, 47833200849, 125395149294, 328724391241, 861753701567, 2259094233704

Offset: 1

Author

Alford Arnold, Apr 22 2006

Keywords

• nonn

Comments

Sherman Stein and A006156 count ordered squarefree(twin-free) ternary words. A060688 counts the dissimilar cases essentially by dividing by 3! (the number of ways to permute a,b,c). A051041 counts ordered squarefree quaternary words. A118311 counts the dissimilar cases (beginning with the 4th term) by dividing A051041 by 4!.

Examples

			a(1) = 1 because a,b,c and d are similar.
a(2) = 1 because aa is not squarefree; so ab is the only valid case.
a(3) = 2 counting aba and abc.
a(4) = 4 counting abac, abca, abcb and abcd.
a(5) = 11 counting abaca,abacb,abcab,abcac,abcba,abacd,abcad,abcbd,abcda,abcdb and abcdc.
		

References

• Sherman Stein, How The Other Half Thinks, 2001, page 149.

Crossrefs

Cf. A006156, A060688, A051041.

Extensions

a(16)-a(25) from Max Alekseyev, Jul 03 2006

a(26)-a(30) from Giovanni Resta, Mar 20 2020