

A104546


Triangle read by rows: T(n,k) is the number of Schroeder paths of length 2n and having k platforms (i.e., UHD, UHHD, UHHHD, ..., where U=(1,1), D=(1,1), H=(2,0)).


4



1, 2, 5, 1, 16, 6, 60, 29, 1, 245, 138, 11, 1051, 670, 84, 1, 4660, 3319, 562, 17, 21174, 16691, 3536, 184, 1, 98072, 84864, 21510, 1628, 24, 461330, 435048, 128134, 12860, 345, 1, 2197997, 2244532, 752486, 94534, 3865, 32, 10585173, 11639558, 4373658
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OFFSET

0,2


COMMENTS

A Schroeder path is a lattice path starting from (0,0), ending at a point on the xaxis, consisting only of steps U=(1,1), D=(1,1) and H=(2,0) and never going below the xaxis. Schroeder paths are counted by the large Schroeder numbers (A006318).
Row n contains 1 + floor(n/2) terms.
Row sums are the large Schroeder numbers (A006318).
Column 0 is A104547.


LINKS

Alois P. Heinz, Rows n = 0..200, flattened


FORMULA

G.f.: G = G(t,z) satisfies G = 1 + zG + zG(G + (t1)z/(1z)).


EXAMPLE

Triangle starts:
1;
2;
5, 1;
16, 6;
60, 29, 1;
T(3,1) = 6 because we have H(UHD), UD(UHD), (UHD)H, (UHD)UD, (UHHD), U(UHD)D; the platforms are shown between parentheses.


CROSSREFS

Cf. A006318, A104547.
Sequence in context: A111797 A122104 A216121 * A121632 A186361 A197365
Adjacent sequences: A104543 A104544 A104545 * A104547 A104548 A104549


KEYWORD

nonn,tabf


AUTHOR

Emeric Deutsch, Mar 14 2005


STATUS

approved



