A111123 Number of 2's in n-th "Kolakoski" string defined in A054349.

1, 2, 2, 3, 5, 8, 11, 16, 25, 38, 57, 85, 127, 192, 289, 430, 644, 966, 1450, 2173, 3263, 4899, 7341, 11022, 16526, 24802, 37201, 55808, 83702, 125541, 188301, 282444, 423683, 635569, 953356, 1429969, 2144990, 3217454, 4826176, 7239129, 10858479, 16287972, 24431890

Offset: 0

Author

Benoit Cloitre, Oct 16 2005

Keywords

• nonn

Comments

Also the number of terms in n-th string (starting from n=3) when representing A000002 as a tree. Each branch of this tree is a string. Starting from n=3, each 1 in n-th string generates either 1 or 2 in (n+1)-th string and each 2 in n-th string generates either 11 or 22 in (n+1)-th string based on the previously generated term of either 2 or 1. Hence, the number of terms in (n+1)-th string is the sum of all terms in n-th string. - Rakesh Khanna A, May 24 2020

Links

• Rakesh Khanna A, Table of n, a(n) for n = 0..59

Crossrefs

Cf. A001083, A042942, A054349, A111124 (number of 1's).

Programs

Mathematica

l = { (*terms in A042942*) }; For[i = 2, i <= Length[l], i++, Print[l[[i]] - l[[i - 1]]]]

Formula

a(0) + a(1) + ... + a(n) = A042942(n+2) - 1.

a(n) = A001083(n+4) - A001083(n+3). - Benoit Cloitre, Nov 07 2010

Extensions

More terms from and offset changed to 0 by Jinyuan Wang, Apr 03 2020