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%I #13 Jan 08 2018 15:56:13
%S 1,2,4,8,16,32,52,88,134,184,254,342,422,530,658,770,922,1090,1248,
%T 1438,1640,1834,2090,2334,2570,2842,3158,3432,3762,4104,4438,4810,
%U 5210,5568,6022,6420,6858,7344,7852,8292,8816,9352,9894,10448,11056,11584,12274,12880,13498,14168,14886,15530,16298,17002,17754
%N Number of length-n binary strings where every prefix is either a palindrome, or the concatenation of two palindromes.
%e For n = 6 the 12 missing strings are 001011,001101,010011,010110,011001,011010 and their bitwise complements.
%p g:= proc(L) local k;
%p if L = ListTools:-Reverse(L) then return true fi;
%p for k from 1 to nops(L)-1 do
%p if L[1..k]=ListTools:-Reverse(L[1..k]) and L[k+1..-1] = ListTools:-Reverse(L[k+1..-1]) then return true fi;
%p od:
%p false
%p end proc:
%p A[0]:= 1: S:= [[]]:
%p for n from 1 to 55 do
%p S:= select(g, map(t -> ([op(t),0],[op(t),1]), S));
%p A[n]:= nops(S);
%p od:
%p seq(A[i],i=0..55); # _Robert Israel_, Jan 03 2018
%K nonn
%O 0,2
%A _Jeffrey Shallit_, Jan 03 2018
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