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A124389
A square array of Kolakoski string lengths, read by antidiagonals.
1
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.
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
KEYWORD
easy,nonn,tabl
AUTHOR
Paul Barry, Oct 30 2006
STATUS
approved