This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A362063 #15 Jun 15 2023 11:09:03 %S A362063 1,1,2,4,8,16,31,60,111,205,364,647,1110,1908,3190,5345,8743,14352, %T A362063 23090,37232,59113,94079,147531,232073,360750,561692,865823,1338269, %U A362063 2047388,3139690,4781349,7281656,11021651,16716751,25178531,37994309,57046272 %N A362063 Number of 2-balanced binary words of length n with respect to the permutations of the symbols. %C A362063 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 A362063 Can be interpreted as a number of 2-balanced binary words with the prefix "0". %F A362063 a(n) = A274005(n)/2 for n>0, since A274005 is the number of all binary 2-balanced words of given length. %e A362063 a(3) = 4 since 000, 001, 010 and 011 are 2-balanced. %e A362063 a(6) = 31 since all words of form 0XXXXX are 2-balanced, except the word 000111. %Y A362063 A274005 is the number of all binary 2-balanced words with given length. %Y A362063 A005598 is the number of all binary balanced (1-balanced) words with given length. %K A362063 nonn %O A362063 0,3 %A A362063 Dominika Datko, communicated by _Bartlomiej Pawlik_, Apr 07 2023