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A122680
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Number of possible basketball games that end in a tie (n:n). Equivalently, the number of walks on the square lattice from (0,0) to (n,n) where the allowed steps are {(1,0),(2,0),(3,0), (0,1),(0,2),(0,3)}.
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1
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1, 2, 14, 106, 784, 6040, 47332, 375196, 3001966, 24190148, 196034522, 1596030740, 13044459766, 106961525744, 879512777006, 7249483605580, 59881171431050, 495545064567260, 4107666916668414, 34099685718629264, 283454909832384416, 2359069189033880228
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OFFSET
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0,2
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LINKS
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EXAMPLE
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a(1) = 2 because the number of ways of getting the score to be (1,1) is
(0,0) -> (1,0) -> (1,1),
(0,0) -> (0,1) -> (1,1).
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MAPLE
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b:= proc(x, y) option remember; `if`(x<0 or y<0, 0,
`if`([x, y]=[0, 0], 1, add(b(x-i, y) +b(x, y-i), i=1..3)))
end:
a:= n-> b(n, n):
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MATHEMATICA
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b[x_, y_] := b[x, y] = If[x < 0 || y < 0, 0, If[{x, y} == {0, 0}, 1, Sum[b[x - i, y] + b[x, y - i], {i, 3}]]];
a[n_] := b[n, n];
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CROSSREFS
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KEYWORD
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nonn,walk
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AUTHOR
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STATUS
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approved
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