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%I #15 Jun 15 2023 11:09:03
%S 1,1,2,4,8,16,31,60,111,205,364,647,1110,1908,3190,5345,8743,14352,
%T 23090,37232,59113,94079,147531,232073,360750,561692,865823,1338269,
%U 2047388,3139690,4781349,7281656,11021651,16716751,25178531,37994309,57046272
%N Number of 2-balanced binary words of length n with respect to the permutations of the symbols.
%C 2-balanced binary words are here defined as the binary words with such property that the sum of each subblock differs by at most 2 from every other subblock of the same length.
%C Can be interpreted as a number of 2-balanced binary words with the prefix "0".
%F a(n) = A274005(n)/2 for n>0, since A274005 is the number of all binary 2-balanced words of given length.
%e a(3) = 4 since 000, 001, 010 and 011 are 2-balanced.
%e a(6) = 31 since all words of form 0XXXXX are 2-balanced, except the word 000111.
%Y A274005 is the number of all binary 2-balanced words with given length.
%Y A005598 is the number of all binary balanced (1-balanced) words with given length.
%K nonn
%O 0,3
%A Dominika Datko, communicated by _Bartlomiej Pawlik_, Apr 07 2023