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A096587
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Triangle read by rows: T(n,k)=number of Catalan knight paths in Quadrant I from (0,0) to (n,k). A Catalan knight moves (1 right and 2 up) or (1 right and 2 down) or (2 right and 1 up) or (2 right and 1 down).
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6
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1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 2, 2, 0, 0, 1, 3, 3, 1, 2, 3, 3, 0, 0, 1, 2, 4, 9, 8, 3, 3, 4, 4, 0, 0, 1, 12, 12, 10, 11, 18, 15, 6, 4, 5, 5, 0, 0, 1, 14, 22, 42, 39, 27, 22, 30, 24, 10, 5, 6, 6, 0, 0, 1, 54, 61, 64, 72, 98, 87, 56, 38, 45, 35, 15, 6, 7, 7, 0, 0, 1, 86, 128, 213, 217, 181, 167
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OFFSET
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1,12
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COMMENTS
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A005220=Column 1; A005201=Column 2.
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LINKS
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Table of n, a(n) for n=1..87.
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FORMULA
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T(0, 0)=1; T(1, 2)=1; for n>=2, T(n, 0)=T(n-2, 1)+T(n-1, 2), T(n, 1)=T(n-2, 0)+T(n-2, 2)+T(n-1, 3); for k>=2, T(n, k)=T(n-2, k-1)+T(n-2, k+1)+T(n-1, k-2)+T(n-1, k+2).
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EXAMPLE
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Rows:
1
0 0 1
1 1 0 0 1
0 1 2 2 0 0 1
T(3,2) counts these paths: (0,0)-(1,2)-(2,0)-(3,2)
and (0,0)-(1,2)-(2,4)-(3,2).
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CROSSREFS
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Cf. A005220, A005201, A096588.
Sequence in context: A225927 A029392 A035379 * A136438 A059848 A036865
Adjacent sequences: A096584 A096585 A096586 * A096588 A096589 A096590
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling, Jun 28 2004
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STATUS
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approved
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