A216226 Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=1 or if k-n>=4, 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, 0, 1, 1, 0, 1, 2, 0, 0, 0, 3, 2, 0, 0, 0, 3, 5, 0, 0, 0, 0, 0, 8, 5, 0, 0, 0, 0, 0, 8, 13, 0, 0, 0, 0, 0, 0, 0, 21, 13, 0, 0, 0, 0, 0, 0, 0, 21, 34, 0, 0, 0, 0, 0, 0, 0, 0, 0, 55, 34, 0, 0, 0, 0, 0

Offset

0,8

Links

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

Formula

T(n,n) = A000045(2*n-1) = A001519(n).

T(n,n+1) = A000045(2*n+1) = A001519(n+1).

T(n,n+2) = T(n,n+3) = A000045(2*n+2) = A001906(n+1).

Sum_{k, 0<=k<=n} T(n-k,k) = A000045(n+1).

Sum_{k, k>=0} T(n,k) = A000285(2*n+1).

Sum_{n, n>=0} T(n,k) = A000285(2*k-2), k>=2.

Example

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

Crossrefs

Cf. A000045 (Fibonacci numbers), A000285, A001519, A001906, A068914

Cf. Similar sequences: A216201, A216210, A216216, A216218, A216219, A216220, A216228, A216229, A216230

Sequence in context: A113503 A082507 A132349 * A123391 A212172 A275812

Adjacent sequences: A216223 A216224 A216225 * A216227 A216228 A216229

Keyword

nonn,tabl

Author

Philippe Deléham, Mar 13 2013

Status

approved