

A111123


Number of 2's in nth "Kolakoski" string defined in A054349.


2



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
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OFFSET

0,2


COMMENTS

Also the number of terms in nth 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 nth string generates either 1 or 2 in (n+1)th string and each 2 in nth 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 nth string.  Rakesh Khanna A, May 24 2020


LINKS

Table of n, a(n) for n=0..42.


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



