A216210 Square array T read by antidiagonals: T(n,k) = 0 if n-k>=4 or if k-n>=4, T(3,0) = T(2,0) = TT(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, 1, 1, 3, 3, 1, 0, 4, 6, 4, 0, 0, 4, 10, 10, 4, 0, 0, 0, 14, 20, 14, 0, 0, 0, 0, 14, 34, 34, 14, 0, 0, 0, 0, 0, 48, 68, 48, 0, 0, 0, 0, 0, 0, 48, 116, 116, 48, 0, 0, 0, 0, 0, 0, 0, 164, 232, 164, 0, 0, 0, 0

Offset

0,5

Links

Table of n, a(n) for n=0..65.

Formula

T(n,n) = A006012(n).

T(n,n+1) = T(n+1,n) = A007052(n).

T(n,n+2) = T(n,n+3) = T(n+2,n) = T(n+3,n) = A007070(n).

Sum_{k, 0<=k<=n} T(n-k,k) = A068912(n).

Example

Square array begins:
1, 1,  1,  1,   0,   0,   0,    0,    0, 0, ... row n=0
1, 2,  3,  4,   4,   0,   0,    0,    0, 0, ... row n=1
1, 3,  6, 10,  14,  14,   0,    0,    0, 0, ... row n=2
1, 4, 10, 20,  34,  48,  48,    0,    0, 0, ... row n=3
0, 4, 14, 34,  68, 116, 164,  164,    0, 0, ... row n=4
0, 0, 14, 48, 116, 232, 396,  560,  560, 0, ... row n=5
0, 0,  0, 48, 164, 396, 792, 1352, 1912, 1912,  row n=6
...

Crossrefs

Cf. A006012, A007052, A007070, A068912

Sequence in context: A048805 A204015 A370140 * A186332 A129571 A180180

Adjacent sequences: A216207 A216208 A216209 * A216211 A216212 A216213

Keyword

nonn,tabl

Author

Philippe Deléham, Mar 12 2013

Status

approved