A362063 Number of 2-balanced binary words of length n with respect to the permutations of the symbols.

1, 1, 2, 4, 8, 16, 31, 60, 111, 205, 364, 647, 1110, 1908, 3190, 5345, 8743, 14352, 23090, 37232, 59113, 94079, 147531, 232073, 360750, 561692, 865823, 1338269, 2047388, 3139690, 4781349, 7281656, 11021651, 16716751, 25178531, 37994309, 57046272

Offset: 0

Author

Dominika Datko, communicated by Bartlomiej Pawlik, Apr 07 2023

Keywords

• nonn

Comments

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.

Can be interpreted as a number of 2-balanced binary words with the prefix "0".

Examples

			a(3) = 4 since 000, 001, 010 and 011 are 2-balanced.
a(6) = 31 since all words of form 0XXXXX are 2-balanced, except the word 000111.
		

Crossrefs

A274005 is the number of all binary 2-balanced words with given length.

A005598 is the number of all binary balanced (1-balanced) words with given length.

Formula

a(n) = A274005(n)/2 for n>0, since A274005 is the number of all binary 2-balanced words of given length.