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A080935
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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 all values less than or equal to k.
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3
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1, 1, 2, 1, 4, 5, 1, 8, 13, 14, 1, 16, 34, 41, 42, 1, 32, 89, 122, 131, 132, 1, 64, 233, 365, 417, 428, 429, 1, 128, 610, 1094, 1341, 1416, 1429, 1430, 1, 256, 1597, 3281, 4334, 4744, 4846, 4861, 4862, 1, 512, 4181, 9842, 14041, 16016, 16645, 16778, 16795
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OFFSET
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1,3
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LINKS
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Table of n, a(n) for n=1..54.
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FORMULA
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For 1<=k<=n, T(n, k) =A080934(n, k) =T(n, k-1)+A080936(n, k).
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EXAMPLE
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Rows start: 1; 1,2; 1,4,5; 1,8,13,14; 1,16,34,41,42; etc. T(3,2)=4 since the paths of length 2*3 (7 points) with all values less than or equal to 2 can take the routes 0101010, 0101210, 0121010 or 0121210, but not 0123210.
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CROSSREFS
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Cf. A000108, A079214, A080934, A080936.
Sequence in context: A211561 A134248 A248670 * A102661 A121574 A117317
Adjacent sequences: A080932 A080933 A080934 * A080936 A080937 A080938
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KEYWORD
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nonn,tabl
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AUTHOR
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Henry Bottomley, Feb 25 2003
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STATUS
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approved
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