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

0,3

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".

Links

Table of n, a(n) for n=0..36.

Formula

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

Example

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.

Sequence in context: A334636 A299026 A007800 * A309982 A102726 A188900

Adjacent sequences: A362060 A362061 A362062 * A362064 A362065 A362066

Keyword

nonn

Author

Dominika Datko, communicated by Bartlomiej Pawlik, Apr 07 2023

Status

approved