OFFSET
1,2
LINKS
Jean-Luc Baril, Pamela E. Harris, and José L. Ramírez, Flattened Catalan Words, arXiv:2405.05357 [math.CO], 2024. See pp. 19-20.
FORMULA
EXAMPLE
The irregular triangle begins:
1;
2;
4, 1;
9, 5;
22, 18, 1;
56, 58, 8;
145, 178, 41, 1;
378, 532, 173, 11;
988, 1563, 656, 73, 1;
...
T(6,2) = 8 since there are 8 flattened Catalan words of length 6 with 2 short peaks: 001010, 010100, 010101, 010010, 010120, 010121, 012010, and 012121.
MATHEMATICA
T[n_, k_]:=SeriesCoefficient[x(1-2x)/((1-x)(1-3x+x^2(1-y))), {x, 0, n}, {y, 0, k}]; Table[T[n, k], {n, 14}, {k, 0, Floor[(n-1)/2]}]//Flatten
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Stefano Spezia, May 15 2024
STATUS
approved