A216228 Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=1 or if k-n>=3, T(0,0) = T(0,1) = T(0,2) = 1, T(n,k) = T(n-1,k) + T(n,k-1).

1, 1, 0, 1, 1, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 32

Offset: 0

Author

Philippe Deléham, Mar 13 2013

Keywords

• nonn
• tabl

Comments

An arithmetic hexagon of E. Lucas.

Examples

			Square array begins:
1, 1, 1, 0, 0,  0,  0,  0, ... row n=0
0, 1, 2, 2, 0,  0,  0,  0, ... row n=1
0, 0, 2, 4, 4,  0,  0,  0, ... row n=2
0, 0, 0, 4, 8,  8,  0,  0, ... row n=3
0, 0, 0, 0, 8, 16, 16,  0, ... row n=4
0, 0, 0, 0, 0, 16, 32, 32, ... row n=5
...
		

References

• E. Lucas, Théorie des nombres, Albert Blanchard, Paris 1958, Tome 1, p.89

Links

• E. Lucas, Théorie des nombres, Tome 1, Jacques Gabay, Paris, 1991, p.89

Crossrefs

Cf. A000079, A011782, A016116, A068914, A084215.

Formula

T(n,n) = A011782(n).

T(n,n+1) = T(n,n+2) = 2^n = A000079(n).

Sum_{k, 0<=k<=n} T(n-k,k) = A016116(n).

Sum_{n, n>=0} T(n,k) = A084215(k).

Sum_{k, k>=0} T(n,k) = A084215(n+1), n>=1.