%I A102726
%S A102726 1,1,2,4,8,16,31,60,114,214,398,732,1334,2410,4321,7688,13590,23869,
%T A102726 41686,72405,125144,215286,368778,629156,1069396,1811336,3058130,
%U A102726 5147484,8639976,14463901,24154348,40244877,66911558,111026746
%N A102726 Number of compositions of the integer n into positive parts that avoid 
               a fixed pattern of three letters.
%C A102726 The sequence is the same no matter which of the six patterns of three 
               letters is chosen as the one to be avoided.
%D A102726 Herbert S. Wilf, Pattern avoidance in compositions and multiset permutations, 
               preprint, 2005.
%H A102726 M. Elder and V. Vatter, <a href="http://arXiv.org/abs/math.CO/0505504">
               Problems and conjectures presented at the third international conference 
               on permutation petterns</a>
%F A102726 G.f.: sum((1/(1-x^i))*prod((1-x^i)/((1-x^(j-i))*(1-x^i-x^j)), j=1..infinity; 
               j not equal to i), i=1..infinity)
%e A102726 a(6)=31 because there are 32 compositions of 6 into positive parts and 
               only one of these, namely 6=1+2+3, contains the pattern (123), the 
               other 31 compositions of 6 avoid that pattern.
%Y A102726 Sequence in context: A000128 A106399 A007800 this_sequence A118891 A107066 
               A141019
%Y A102726 Adjacent sequences: A102723 A102724 A102725 this_sequence A102727 A102728 
               A102729
%K A102726 easy,nonn
%O A102726 1,3
%A A102726 Herbert S. Wilf (wilf(AT)math.upenn.edu), Feb 07 2005
%E A102726 More terms from Ralf Stephan (ralf(AT)ark.in-berlin.de), May 27 2005