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A099330
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Number of Catalan knight paths from (0,0) to (n,2) 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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3
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0, 1, 0, 1, 1, 5, 6, 14, 18, 43, 70, 147, 243, 475, 828, 1596, 2852, 5365, 9676, 18037, 32853, 60929, 111394, 205770, 377142, 695519, 1276818, 2351975, 4320935, 7954167, 14620472, 26904824, 49467208, 91010153, 167357080, 307868201
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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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 6 paths from (0,0) to (6,2); the final move in 1
path is from the point (4,3), the final move in 3 paths
is from (4,1) and and the final move in the other 2 paths
is from (5,0).
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CROSSREFS
| Cf. A099328, A099329, A099331.
Sequence in context: A059176 A030356 A138937 * A180686 A145491 A060724
Adjacent sequences: A099327 A099328 A099329 * A099331 A099332 A099333
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu), Oct 12 2004
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