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A201076
Irregular triangle read by rows: number of {0,2}-shifted Schroeder paths of length n and area k.
3
1, 1, 1, 2, 0, 1, 2, 3, 3, 0, 1, 2, 3, 6, 7, 7, 5, 0, 0, 1, 2, 3, 6, 10, 13, 16, 20, 19, 15, 8, 0, 0, 1, 2, 3, 6, 10, 16, 22, 29, 39, 48, 53, 56, 57, 46, 30, 13, 0, 0, 0, 1, 2, 3, 6, 10, 16, 25, 35, 48, 66, 85, 106, 127, 147, 167, 179, 178, 168, 146, 103, 58, 21, 0, 0, 0
OFFSET
0,4
LINKS
Brian Drake, Limits of areas under lattice paths, Discrete Math. 309 (2009), no. 12, 3936-3953.
EXAMPLE
Triangle begins
1
1
1 2 0
1 2 3 3 0
1 2 3 6 7 7 5 0 0
1 2 3 6 10 13 16 20 19 15 8 0 0
...
MATHEMATICA
gf = Expand /@ FixedPoint[1 + (q x + q^2 x^2) # (Normal@# /. {x :> q^2 x}) + O[x]^8 &, 0];
Flatten[Reverse[CoefficientList[#, q]][[;; ;; 2]] & /@ CoefficientList[gf, x]] (* Andrey Zabolotskiy, Jan 02 2024 *)
CROSSREFS
Row sums give A052709. Rows converge to A101277.
Cf. S-shifted Schroeder paths for various S: A201075 {0,1}, A201079 {0,2,4,6...}, A201080 {0,1,3,5...}, A201159 {0,1,2}.
Sequence in context: A119464 A214568 A107017 * A201079 A318601 A306814
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Nov 26 2011
EXTENSIONS
Row 5 corrected, rows 6-7 added by Andrey Zabolotskiy, Jan 02 2024
STATUS
approved