A216229 Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=2 or if k-n>=3, 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, 0, 0, 3, 2, 0, 0, 3, 5, 0, 0, 0, 0, 8, 5, 0, 0, 0, 0, 8, 13, 0, 0, 0, 0, 0, 0, 21, 13, 0, 0, 0, 0, 0, 0, 21, 34, 0, 0, 0, 0, 0, 0, 0, 0, 55, 34, 0, 0, 0, 0, 0, 0, 0, 0, 55, 89, 0, 0, 0, 0, 0, 0, 0

Offset

0,5

Links

Table of n, a(n) for n=0..67.

Formula

T(n,n) = T(n+1,n) = A001519(n+1).

T(n,n+1) = T(n,n+2) = A001906(n+1).

Sum_{k, 0<=k<=n} T(n-k,k) = A000045(n+2).

T(n,k) = A216226(n,k+1).

Example

Square array begins:
1, 1, 1,  0,  0,  0,   0,   0, ... row n=0
1, 2, 3,  3,  0,  0,   0,   0, ... row n=1
0, 2, 5,  8,  8,  0,   0,   0, ... row n=2
0, 0, 5, 13, 21, 21,   0,   0, ... row n=3
0, 0, 0, 13, 34, 55,  55,   0, ... row n=4
0, 0, 0,  0, 34, 89, 144, 144, ... row n=5
...

Crossrefs

Cf. A000045 (Fibonacci numbers), A001519, A001906, A216226

Sequence in context: A113411 A260110 A261115 * A224777 A259827 A143161

Adjacent sequences: A216226 A216227 A216228 * A216230 A216231 A216232

Keyword

nonn,tabl

Author

Philippe Deléham, Mar 14 2013

Status

approved