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Search: id:A080936
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| A080936 |
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Triangle read by rows of number of Catalan paths (nonnegative, starting and ending at 0, step +/-1) of 2n steps with highest value equal to k. |
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+0
3
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| 1, 1, 1, 1, 3, 1, 1, 7, 5, 1, 1, 15, 18, 7, 1, 1, 31, 57, 33, 9, 1, 1, 63, 169, 132, 52, 11, 1, 1, 127, 482, 484, 247, 75, 13, 1, 1, 255, 1341, 1684, 1053, 410, 102, 15, 1, 1, 511, 3669, 5661, 4199, 1975, 629, 133, 17, 1, 1, 1023, 9922, 18579, 16017, 8778, 3366, 912, 168
(list; table; graph; listen)
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OFFSET
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1,5
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FORMULA
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T(n, k) =A080934(n, k)-A080934(n, k-1).
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EXAMPLE
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Rows start: 1; 1,1; 1,3,1; 1,7,5,1; 1,15,18,7,1; 1,31,57,33,9,1; 1,63,169,132,52,11,1; etc. T(3,2)=3 since the paths of length 2*3=6 (7 points) with a maximum equal to 2 can take the routes 0101210, 0121010 or 0121210, but not 0101010 or 0123210.
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CROSSREFS
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Cf. A000108 (row sums), A079214, A080934, A080935.
Sequence in context: A108625 A112857 A118801 this_sequence A094507 A065625 A154341
Adjacent sequences: A080933 A080934 A080935 this_sequence A080937 A080938 A080939
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KEYWORD
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nonn,tabl
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Feb 25 2003
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