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%I #10 Apr 06 2020 19:14:13
%S 2,2,4,12,24,12,28,4,16,60,4,24,140,2,32,230,1112,36,332,4
%N a(n) is the number of length n strings over a two-letter alphabet that have a minimum palindromic partition size of A090701(n).
%C A "minimum palindromic partition size" of a string is the fewest number of palindromes that the string can be partitioned into.
%C All terms are even because the letters of the alphabet can be swapped (e.g., "101100" can become "010011".)
%e The a(6) = 12 six-character strings that require A090701(6) = 3 partitions are:
%e 100101 via (1001)(0)(1),
%e 100110 via (1001)(1)(0),
%e 101001 via (1)(0)(1001),
%e 101100 via (101)(1)(00),
%e 110010 via (1)(1001)(0),
%e 110100 via (11)(010)(0),
%e along with the six strings made from swapping the 0's and 1's.
%Y Cf. A090701.
%K nonn,more
%O 1,1
%A _Peter Kagey_, Jan 19 2018
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