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

0,2

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

Formula

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

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

Mathematica

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

Crossrefs

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

Sequence in context: A267419 A076777 A240210 * A261091 A179523 A087729

Adjacent sequences: A111120 A111121 A111122 * A111124 A111125 A111126

Keyword

nonn

Author

Benoit Cloitre, Oct 16 2005

Extensions

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

Status

approved