cp's OEIS Frontend

A065078 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].

%I A065078 #10 Apr 11 2013 13:22:18
%S A065078 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,
%T A065078 2681,10488,24661,1,7,98,962,6883,37367,149743,365613,1,8,140,1715,
%U A065078 15318,105731,573051,2336243,5863881,1,9,192,2856,30840,258604,1742770
%N A065078 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].
%C A065078 Number of paths to T[n,m,m] counted from the bottom plane (or T[n,m,0]).
%H A065078 Wouter Meeussen, <a href="/A065078/a065078.txt">Further comments on this sequence</a>
%F A065078 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}]
%e A065078 [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.
%e A065078 Triangle begins
%e A065078 1;
%e A065078 1, 1;
%e A065078 1, 2, 3;
%e A065078 1, 3, 10, 18;
%e A065078 1, 4, 22, 79, 162;
%Y A065078 Last number in each row is A065058.
%Y A065078 Cf. A005789, A065057.
%K A065078 nonn,tabl
%O A065078 0,5
%A A065078 _Wouter Meeussen_, Nov 09 2001