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A080938
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Number of Catalan paths (nonnegative, starting and ending at 0, step +/-1) of 2n steps with all values less than or equal to 7.
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4
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1, 1, 2, 5, 14, 42, 132, 429, 1429, 4846, 16645, 57686, 201158, 704420, 2473785, 8704089, 30664890, 108126325, 381478030, 1346396146, 4753200932, 16783118309, 59266297613, 209302921830, 739203970773, 2610763825782, 9221050139566
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| a(n) =A080934(n, 7)
G.f.: (1-6x+10x^2-4x^3)/(1-7x+15x^2-10x^3+x^4). - Ralf Stephan (ralf(AT)ark.in-berlin.de), May 13 2003
a(n)=7a(n-1)-15a(n-2)+10a(n-3)-a(n-4) - Herbert Kociemba (kociemba(AT)t-online.de), Jun 13 2004
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CROSSREFS
| Cf. A000007, A000012, A011782, A001519, A007051, A080937, A024175, A080938, A033191 which essentially provide the same sequence for different limits and tend to A000108.
Sequence in context: A054393 A036768 A058094 * A054394 A036769 A033191
Adjacent sequences: A080935 A080936 A080937 * A080939 A080940 A080941
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KEYWORD
| nonn
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Feb 25 2003
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