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Search: id:A104546
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| A104546 |
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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)). |
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+0
4
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| 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
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0,2
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COMMENT
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A Schroeder path is a lattice path starting from (0,0), ending at a point on the x-axis, consisting only of steps U=(1,1), D=(1,-1) and H=(2,0) and never going below the x-axis. 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.
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FORMULA
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G.f.=G=G(t, z) satisfies G=1+zG+zG[G+(t-1)z/(1-z)].
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EXAMPLE
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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.
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CROSSREFS
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Cf. A006318, A104547.
Sequence in context: A119518 A111797 A122104 this_sequence A121632 A121579 A106852
Adjacent sequences: A104543 A104544 A104545 this_sequence A104547 A104548 A104549
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KEYWORD
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nonn,tabf
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 14 2005
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