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Search: id:A050157
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| A050157 |
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T(n,k)=S(2n,n,k), 0<=k<=n, n >= 0, where S(p,q,r)=number of upright paths from (0,0) to (p,p-q) that do not rise above the line y=x-r. |
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11
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| 1, 1, 2, 2, 5, 6, 5, 14, 19, 20, 14, 42, 62, 69, 70, 42, 132, 207, 242, 251, 252, 132, 429, 704, 858, 912, 923, 924, 429, 1430, 2431, 3068, 3341, 3418, 3431, 3432, 1430, 4862, 8502, 11050, 12310, 12750, 12854, 12869, 12870
(list; table; graph; listen)
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OFFSET
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0,3
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COMMENT
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Let V=(e(1),...,e(n)) consist of q 1's and p-q 0's; let V(h)=(e(1),...,e(h)) and m(h)=(#1's in V(h))-(#0's in V(h)) for h=1,...,n. Then S(p,q,r)=number of V having r>=max{m(h)}.
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FORMULA
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T(n, k)=Sum{t(n, j): 0<=j<=k}, array t as in A039599.
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EXAMPLE
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Rows: {1}; {1,2}; {2,5,6}; ...
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CROSSREFS
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Sequence in context: A068763 A112573 A120406 this_sequence A054255 A063177 A034803
Adjacent sequences: A050154 A050155 A050156 this_sequence A050158 A050159 A050160
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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