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 A289323 #21 Jul 07 2017 03:29:25 %S A289323 -1,0,0,0,0,-2,0,0,-2,0,-2,0,-6,6,0,6,44,26,-20,-48,52,58,104,-82, %T A289323 -250,-270,-474,-1864,-3094,-4588,-2534,-7574,-1522,1818,9264,18082, %U A289323 8898,-30500,-20586,-3232,-90522,-127446,-231384,-83574,-87364,267886 %N A289323 Number of twos minus number of ones in the first 2^n entries of the Kolakoski sequence, A000002. %C A289323 This is equivalent to A289322, since a(n) = (#twos)-(#ones) = 2^n-2*(#ones) in the first 2^n entries of A000002. %C A289323 For example, a(5)=15-17=(32-17)-17=32-2*17=-2 because there are 15 twos and 17 ones in the first 32=2^5 entries of A000002. %C A289323 The entries in this sequence appear to be of order 2^(n/2), whereas the entries in A289322 are larger (of order 2^n). %D A289323 See references for A289322. %H A289323 Richard P. Brent, <a href="/A289323/b289323.txt">Table of n, a(n) for n = 0..64</a> %F A289323 a(n) = 2^n - 2*A289322(n) = -A088568(2^n) = 2*A054353(2^n) - 3*2^n = 2^n - 2*A156077(2^n). %e A289323 The first 32 entries of the Kolakoski sequence, A000002, are 12211212212211211221211212211211. From this we see that a(5)=15-17=-2, since among the first 2^5 letters, 15 of them are twos and 17 of them are ones. %Y A289323 Cf. A000002, A054353, A074286, A088568, A156077, A289322. %K A289323 sign %O A289323 0,6 %A A289323 _Richard P. Brent_, Jul 05 2017