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Search: id:A065078
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| A065078 |
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Triangle read by rows: a(n,m) = T[n,m,m] where T[i,j,k] is the 3-dimensional pyramid defined by T[n,m,0]=1 and 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]. |
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+0
2
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| 1, 1, 1, 1, 2, 3, 1, 3, 10, 18, 1, 4, 22, 79, 162, 1, 5, 40, 220, 831, 1851, 1, 6, 65, 492, 2681, 10488, 24661, 1, 7, 98, 962, 6883, 37367, 149743, 365613, 1, 8, 140, 1715, 15318, 105731, 573051, 2336243, 5863881, 1, 9, 192, 2856, 30840, 258604, 1742770
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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Number of paths to T[n,m,m] counted from the bottom plane (or T[n,m,0]).
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LINKS
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Wouter Meeussen, Further comments on this sequence
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FORMULA
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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); Table[T[x, y, y], {x, 0, 10}, {y, 0, x}]
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EXAMPLE
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[3,2,2] can be reached from 3*[1,1,0] + 3*[2,1,0] + 2*[2,2,0] + 1*[3,1,0] + 1*[3,2,0], so a(3,2) = 3 + 3 + 2 + 1 + 1 =10
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CROSSREFS
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Last number in each row is A065058.
Cf. A005789, A065057.
Sequence in context: A135091 A010027 A108990 this_sequence A126744 A122078 A126736
Adjacent sequences: A065075 A065076 A065077 this_sequence A065079 A065080 A065081
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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 09 2001
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