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Search: id:A065058
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| A065058 |
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Number of paths to T[n,n,n] with T[i,j,k]=0 if j>i or k>j and T[i,j,k]=T[i-1,j,k]+T[i,j-1,k]+T[i,j,k-1] and T[i,j,0]=1. |
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+0
3
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| 1, 3, 18, 162, 1851, 24661, 365613, 5863881, 99895425, 1785024645, 33156724734, 635961987570, 12531882072719, 252701147866029, 5198011293931270, 108793300411597194, 2312049376195527621, 49804793378882733343
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Similar to the "3-dimensional Catalan numbers" of A005789, but with paths starting from anywhere on z=0, instead of only from [0,0,0].
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EXAMPLE
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a(3) = 18 because [3,3,3] can be reached from [x,y,0] in the following ways (along non-decreasing paths): 5 [1,1,0] + 5 [2,1,0] + 3 [2,2,0] + 2 [3,1,0] + 2 [3,2,0] + [3,3,0]
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MATHEMATICA
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T[0, 0, 0] := 1; T[x_, y_, z_] := 0 /; (x< y || y< z); T[u_, v_, 0] := 1; T[_, 0, 0] := 1 T[x_, y_, z_] := (T[x, y, z]= T[x-1, y, z]+T[x, y-1, z] +T[x, y, z-1]) /; (y<=x ||z<=y)
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CROSSREFS
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A005789
Sequence in context: A067302 A052182 A115415 this_sequence A032031 A127646 A089466
Adjacent sequences: A065055 A065056 A065057 this_sequence A065059 A065060 A065061
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KEYWORD
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nonn
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AUTHOR
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Wouter Meeussen (wouter.meeussen(AT)pandora.be), Nov 06 2001
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