

A118311


Number of dissimilar squarefree quaternary words of length n.


2



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(twinfree) 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.
Sequence in context: A061860 A093960 A267912 * A132836 A148140 A328139
Adjacent sequences: A118308 A118309 A118310 * A118312 A118313 A118314


KEYWORD

nonn


AUTHOR

Alford Arnold, Apr 22 2006


EXTENSIONS

a(16)a(25) from Max Alekseyev, Jul 03 2006
a(26)a(30) from Giovanni Resta, Mar 20 2020


STATUS

approved



