Search: id:A118311
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%I A118311
%S A118311 1,1,2,4,11,29,77,202,532,1395,3664,9605,25192,66047,173183,453998,
%T A118311 1190259,3120294,8180124,21444290,56217025,147373441,386342414,
%U A118311 1012799936,2655067412
%N A118311 Number of dissimilar square-free quaternary words of length n.
%C A118311 Sherman Stein and A006156 count ordered square-free(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 
               square-free quaternary words. A118311 counts the dissimilar cases 
               (beginning with the 4th term) by dividing A051041 by 4!
%D A118311 Sherman Stein, How The Other Half Thinks, 2001, page 149
%e A118311 a(1) = 1 because a,b,c and d are similar.
%e A118311 a(2) = 1 because aa is not square-free; so ab is the only valid case.
%e A118311 a(3) = 2 counting aba and abc
%e A118311 a(4) = 4 counting abac, abca, abcb and abcd
%e A118311 a(5) = 11 counting abaca,abacb,abcab,abcac,abcba,abacd,abcad,abcbd,abcda,
               abcdb and abcdc
%Y A118311 Cf. A006156, A060688, A051041.
%Y A118311 Sequence in context: A148139 A061860 A093960 this_sequence A132836 A148140 
               A148141
%Y A118311 Adjacent sequences: A118308 A118309 A118310 this_sequence A118312 A118313 
               A118314
%K A118311 nonn
%O A118311 1,3
%A A118311 Alford Arnold (Alford1940(AT)aol.com), Apr 22 2006
%E A118311 a(16)-a(25) from Max Alekseyev (maxale(AT)gmail.com), Jul 03 2006

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