A216216 Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=3 or if k-n>=3, T(2,0) = T(1,0) = T(0,0) = T(0,1) = T(0,2) = 1, T(n,k) = T(n-1,k) + T(n,k-1).

1, 1, 1, 1, 2, 1, 0, 3, 3, 0, 0, 3, 6, 3, 0, 0, 0, 9, 9, 0, 0, 0, 0, 9, 18, 9, 0, 0, 0, 0, 0, 27, 27, 0, 0, 0, 0, 0, 0, 27, 54, 27, 0, 0, 0, 0, 0, 0, 0, 81, 81, 0, 0, 0, 0, 0, 0, 0, 0, 81, 162, 81, 0, 0, 0, 0

Offset: 0

Author

Philippe Deléham, Mar 13 2013

Keywords

• nonn
• tabl

Examples

			Square array begins:
1, 1, 1,  0,  0,   0,   0,   0, 0, ... n = 0
1, 2, 3,  3,  0,   0,   0,   0, 0, ... n = 1
1, 3, 6,  9,  9,   0,   0,   0, 0, ... n = 2
0, 3, 9, 18, 27,  27,   0,   0, 0, ... n = 3
0, 0, 9, 27, 54,  81,  81,   0, 0, ... n = 4
0, 0, 0, 27, 81, 162, 243, 243, 0, ... n = 5
....
		

Crossrefs

Cf. A000244, A025192, A068911, A068913

Formula

T(n,n) = A025192(n).

T(n+1,n) = T(n+2,n) = T(n,n+1) = T(n,n+2) = 3^n = A000244(n).

Sum_{k, 0<=k<=n} T(n-k,k) = A068911(n).