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A099331
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Number of Catalan knight paths from (0,0) to (n,3) 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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0, 0, 0, 2, 1, 4, 3, 12, 16, 40, 56, 122, 197, 408, 695, 1352, 2368, 4512, 8096, 15202, 27529, 51196, 93339, 172852, 316368, 584104, 1071160, 1974458, 3625613, 6677104, 12269359, 22583120, 41513728, 76387712, 140454656, 258398850, 475182353
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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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 3 paths from (0,0) to (6,3); the final move in 1
path is from (4,2) and the final move in the other 2 paths
is from (5,1).
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CROSSREFS
| Cf. A099328, A099329, A099330.
Sequence in context: A032662 A185413 A138509 * A146001 A091879 A036069
Adjacent sequences: A099328 A099329 A099330 * A099332 A099333 A099334
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu), Oct 12 2004
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