A118311 - OEIS

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

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OFFSET

1,3

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!.

REFERENCES

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

LINKS

Table of n, a(n) for n=1..32.

EXAMPLE

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.

CROSSREFS

Cf. A006156, A060688, A051041.