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A201159
Irregular triangle read by rows: number of {0,1,2}-shifted Schroeder paths of length n and area k.
4
1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 4, 5, 5, 5, 3, 1, 1, 1, 2, 2, 4, 5, 8, 10, 12, 13, 15, 17, 16, 13, 9, 4, 1, 1, 1, 2, 2, 4, 5, 8, 10, 15, 18, 23, 27, 34, 40, 47, 52, 56, 57, 57, 56, 50, 39, 26, 14, 5, 1, 1, 1, 2, 2, 4, 5, 8, 10, 15, 18, 26, 32, 42, 50, 63
OFFSET
0,6
LINKS
Brian Drake, Limits of areas under lattice paths, Discrete Math. 309 (2009), no. 12, 3936-3953. See Example 4.
EXAMPLE
Triangle begins
1
1 1
1 1 2 2 1
1 1 2 2 4 5 5 5 3 1
1 1 2 2 4 5 8 10 12 13 15 17 16 13 9 4 1
...
MATHEMATICA
gf = Expand /@ FixedPoint[1 + x # + q x (1 + q x) # (Normal@# /. {x :> q^2 x}) + O[x]^7 &, 0];
Flatten[Reverse[CoefficientList[#, q]] & /@ CoefficientList[gf, x]] (* Andrey Zabolotskiy, Jan 03 2024 *)
CROSSREFS
Row sums are A064641.
Cf. S-shifted Schroeder paths for various S: A201075 {0,1}, A201076 {0,2}, A201079 {0,2,4,6...}, A201080 {0,1,3,5...}.
Sequence in context: A280134 A351256 A143488 * A356225 A047070 A071127
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Nov 27 2011
EXTENSIONS
More terms from Andrey Zabolotskiy, Jan 03 2024
STATUS
approved