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A322329
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Triangle read by rows: T(n,k) is the number of nondecreasing Motzkin prefixes (i.e., left factors of nondecreasing Motzkin paths) of length n and final height k (0 <= k <= n).
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2
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1, 1, 1, 2, 2, 1, 4, 5, 3, 1, 9, 12, 9, 4, 1, 21, 30, 25, 14, 5, 1, 49, 74, 69, 44, 20, 6, 1, 115, 182, 185, 133, 70, 27, 7, 1, 269, 444, 488, 386, 230, 104, 35, 8, 1, 630, 1078, 1266, 1090, 718, 369, 147, 44, 9, 1, 1474, 2605, 3245, 3006, 2161, 1232, 560, 200, 54, 10, 1
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table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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LINKS
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FORMULA
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Riordan array: ((1 - x - 2*x^2 + x^3)/(1 - 2*x - 2*x^2 + 3x^3 - x^5),(x*(1-x)^2*(1+x))/(1 - 2*x - x^2 + 2*x^3 - x^4)).
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EXAMPLE
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Triangle begins:
1;
1, 1;
2, 2, 1;
4, 5, 3, 1;
9, 12, 9, 4, 1;
21, 30, 25, 14, 5, 1;
49, 74, 69, 44, 20, 6, 1;
115, 182, 185, 133, 70, 27, 7, 1;
269, 444, 488, 386, 230, 104, 35, 8, 1;
630, 1078, 1266, 1090, 718, 369, 147, 44, 9, 1;
1474, 2605, 3245, 3006, 2161, 1232, 560, 200, 54, 10, 1;
...
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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