A216220 Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=2 or if k-n>=4, T(1,0) = T(0,0) = T(0,1) = T(0,2) = T(0,3) = 1, T(n,k) = T(n-1,k) + T(n,k-1).

1, 1, 1, 1, 2, 0, 1, 3, 2, 0, 0, 4, 5, 0, 0, 0, 4, 9, 5, 0, 0, 0, 0, 13, 14, 0, 0, 0, 0, 0, 13, 27, 14, 0, 0, 0, 0, 0, 0, 40, 41, 0, 0, 0, 0, 0, 0, 0, 40, 81, 41, 0, 0, 0, 0, 0, 0, 0, 0, 121, 122, 0, 0, 0, 0, 0

Offset: 0

Author

Philippe Deléham, Mar 13 2013

Keywords

• nonn
• tabl

Comments

T(0,2), T(1,1), T(1,2), T(1,3), ... T(n,n), T(n,n+1), T(n,n+2), ... is the sequence A140298.

Examples

			Square array begins:
1, 1, 1,  1,  0,  0,   0,   0, 0, ...
1, 2, 3,  4,  4,  0,   0,   0, 0, ...
0, 2, 5,  9, 13, 13,   0,   0, 0, ...
0, 0, 5, 14, 27, 40,  40,   0, 0, ...
0, 0, 0, 14, 41, 81, 121, 121, 0, ...
...
		

Crossrefs

Cf. A000244, A003462, A007051, A038754,

Formula

T(n,n) = T(n+1,n) = A007051(n).

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

T(n,n+2) = T(n,n+3) = A003462(n+1).

Sum_{k, 0<=k<=n} T(n-k,k) = A038754(n).