OFFSET
0,5
COMMENTS
Number of paths to T[n,m,m] counted from the bottom plane (or T[n,m,0]).
LINKS
Wouter Meeussen, Further comments on this sequence
FORMULA
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}]
EXAMPLE
[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.
Triangle begins
1;
1, 1;
1, 2, 3;
1, 3, 10, 18;
1, 4, 22, 79, 162;
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Wouter Meeussen, Nov 09 2001
STATUS
approved