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A099328
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Number of Catalan knight paths from (0,0) to (n,0) in the region between and on the lines y=0 and y=3. (See A096587 for the definition of Catalan knight.).
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4
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1, 0, 1, 0, 2, 2, 8, 8, 21, 28, 69, 108, 226, 370, 736, 1280, 2473, 4392, 8281, 14920, 27874, 50706, 94088, 171880, 317693, 582116, 1073853, 1970836, 3630914, 6669730, 12279296, 22568896, 41533777, 76360464, 140493041, 258344528, 475256898
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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FORMULA
| Taking A099328 to A099331 as the rows of an array T, the recurrences for these row sequences are given for n>=2 by T(n, 0) = T(n-1, 2) + T(n-2, 1), T(n, 1) = T(n-1, 3) + T(n-2, 0) + T(n-2, 2), T(n, 2) = T(n-1, 0) + T(n-2, 1) + T(n-2, 3), T(n, 3) = T(n-1, 1) + T(n-2, 2), with initial values T(0, 0)=1, T(1, 2)=1.
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EXAMPLE
| a(6) counts 8 paths from (0,0) to (6,0); the final move in 5 of the paths is from the point (5,2) and the final move in the other 3 paths is from (4,1).
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CROSSREFS
| Cf. A099329, A099330, A099331.
Sequence in context: A060818 A082887 A137583 * A073090 A120544 A155950
Adjacent sequences: A099325 A099326 A099327 * A099329 A099330 A099331
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu), Oct 12 2004
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