A216219 Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=5 or if k-n>=5, T(4,0) = T(3,0) = T(2,0) = T(1,0) = T(0,0) = T(0,1) = T(0,2) = T(0,3) = T(0,4) = 1, T(n,k) = T(n-1,k) + T(n,k-1).

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 0, 5, 10, 10, 5, 0, 0, 5, 15, 20, 15, 5, 0, 0, 0, 20, 35, 35, 20, 0, 0, 0, 0, 20, 55, 70, 55, 20, 0, 0, 0, 0, 0, 75, 125, 125, 75, 0, 0, 0, 0, 0, 0, 75, 200, 250, 200

Offset

0,5

Links

Table of n, a(n) for n=0..61.

Formula

T(n,n) = A147748(n).

T(n+1,n) = T(n,n+1) = A081567(n).

T(n+2,n) = T(n,n+2) = A039717(n+1).

T(n+3,n) = T(n+4,n) = T(n,n+3) = T(n,n+4) = A030191(n).

Sum_{k, 0<=k<=n} T(n-k,k) = A068913(4,n) = A216212(n).

Example

Square array begins:
1, 1,  1,  1,   1,   0,   0,   0,    0,    0, 0, ...
1, 2,  3,  4,   5,   5,   0,   0,    0,    0, 0, ...
1, 3,  6, 10,  15,  20,  20,   0,    0,    0, 0, ...
1, 4, 10, 20,  35,  55,  75,  75,    0,    0, 0, ...
1, 5, 15, 35,  70, 125, 200, 275,  275,    0, 0, ...
0, 5, 20, 55, 125, 250, 450, 725, 1000, 1000, 0, ...
0, 0, 20, 75, 200, 450, 900, ...

Crossrefs

Cf. A030191, A039717, A068913, A081567, A147748, A216210, A216212, A216218

Sequence in context: A055216 A216236 A217770 * A180181 A128629 A107065

Adjacent sequences: A216216 A216217 A216218 * A216220 A216221 A216222

Keyword

nonn,tabl

Author

Philippe Deléham, Mar 13 2013

Status

approved