A124389 A square array of Kolakoski string lengths, read by antidiagonals.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3, 5, 1, 1, 1, 1, 7, 5, 7, 1, 1, 1, 1, 9, 17, 7, 9, 1, 1, 1, 1, 17, 25, 31, 9, 11, 1, 1, 1, 1, 25, 61, 49, 49, 11, 13, 1, 1, 1, 1, 43, 109, 145, 81, 71, 13, 15, 1, 1, 1

Offset

0,12

Comments

Rows of square array include A066983,A095342,A095343,A095344. See A066983 for description of Kolakoski strings. Sums of antidiagonals is A124390.

Links

Table of n, a(n) for n=0..65.

Formula

Row k of square array has g.f. (1+x-kx^2)/((1+x)(1-x-kx^2))

Example

Square array begins
1, 1, 1, 1, 1, 1, 1...
1, 1, 1, 3, 3, 7, 9...
1, 1, 1, 5, 5, 17, 25...
1, 1, 1, 7, 7, 31, 49...
1, 1, 1, 9, 9, 49, 81...
1, 1, 1, 11, 11, 71, 121...
1, 1, 1, 13, 13, 97, 169...
As a number triangle, triangle begins
1,
1, 1,
1, 1, 1,
1, 1, 1, 1,
1, 3, 1, 1, 1,
1, 3, 5, 1, 1, 1,
1, 7, 5, 7, 1, 1, 1,
1, 9, 17, 7, 9, 1, 1, 1,
1, 17, 25, 31, 9, 11, 1, 1, 1

Crossrefs

Sequence in context: A331112 A029382 A073780 * A366789 A027023 A052371

Adjacent sequences: A124386 A124387 A124388 * A124390 A124391 A124392

Keyword

easy,nonn,tabl

Author

Paul Barry, Oct 30 2006

Status

approved