OFFSET

1,2

COMMENTS

FORMULA

Introduced here is an array K called the "Kolakoski fan based on a sequence s with initial row w": suppose that s=(s(1),s(2),...) is a sequence of 1's and 2's and that w=(w(1),w(2),...) is a finite or infinite sequence of 1's and 2's. Assume that s(1)=w(1) and that if w(1)=1 then s contains at least one 2. Row 1 of the array K is w. Subsequent rows are defined inductively: the first term of row n is s(n) and the remaining terms are defined by Kolakoski substitution; viz., each number in row n-1 tells the string-length (1 or 2) of the next string in row n, each term being either 1 or 2.

EXAMPLE

s=(1,2,1,2,1,2,1,2,...) and w=1, so the first 7 rows are

1

2

1 1

2 1

1 1 2

2 1 2 2

1 1 2 1 1 2 2

CROSSREFS

KEYWORD

nonn,tabf

AUTHOR

Clark Kimberling, Aug 25 2008

STATUS

approved