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Let p(n, s, x) be predicate that number of occurrences of s's in x >= 2*n - the length of the longest sequence of s's in x. Then a(n)=#{x in {0,1}* | x ends in 0 and p(n,0,x) and (there is no prefix y of x such that p(n,0,y) or p(n,1,y))}.
1

%I #10 May 09 2013 11:06:03

%S 1,5,28,226,2077,20770,222884,2529541

%N Let p(n, s, x) be predicate that number of occurrences of s's in x >= 2*n - the length of the longest sequence of s's in x. Then a(n)=#{x in {0,1}* | x ends in 0 and p(n,0,x) and (there is no prefix y of x such that p(n,0,y) or p(n,1,y))}.

%C a(9)>=29995812 (probably equal to this value)

%K nonn,hard,more

%O 1,2

%A Jonas Wallgren [ jwc(AT)ida.liu.se ]

%E a(7)-a(8) from _Sean A. Irvine_, Nov 14 2010