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%I #14 Nov 29 2019 08:32:18
%S 0,2,4,8,12,22,32
%N Length of shortest binary string containing, as contiguous blocks, all palindromes of length n.
%C Greedy supersequence algorithms give the upper bounds a(7) <= 60, a(8) <= 74, a(9) <= 142, a(10) <= 180, a(11) <= 344, a(12) <= 410, a(13) <= 798. Probably some of these are tight. The value for a(6) was computed by checking all 8! arrangements of the 8 palindromes of length 3, optimizing overlaps. Probably someone with more computing power could compute a(7) (resp., a(8)) by checking all 16! = 20922789888000 arrangements of the palindromes of length 7 (resp., 8).
%e The corresponding strings for 1 <= n <= 6 are:
%e 1: 01
%e 2: 0011
%e 3: 00010111
%e 4: 000011001111
%e 5: 0000010001010111011111
%e 6: 00000011001111000010010110111111
%Y Cf. A057148.
%K nonn,more
%O 0,2
%A _Jeffrey Shallit_, Nov 27 2019
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