A216201 Square array T, read by antidiagonals : T(n,k) = 0 if n-k>=3 or if k-n>=4, T(2,0) = T(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, 0, 0, 4, 6, 3, 0, 0, 4, 10, 9, 0, 0, 0, 0, 14, 19, 9, 0, 0, 0, 0, 14, 33, 28, 0, 0, 0, 0, 0, 0, 47, 61, 28, 0, 0, 0, 0, 0, 0, 47, 108, 89, 0, 0, 0, 0, 0, 0, 0, 0, 155, 197, 89, 0, 0, 0, 0

Offset: 0

Author

Philippe Deléham, Mar 12 2013

Keywords

• nonn
• tabl

Examples

			Square array begins:
1, 1, 1,  1,  0,   0,   0,   0,   0,   0, 0, 0, 0, ... row n = 0
1, 2, 3,  4,  4,   0,   0,   0,   0,   0, 0, 0, 0, ... row n = 1
1, 3, 6, 10, 14,  14,   0,   0,   0,   0, 0, 0, 0, ... row n = 2
0, 3, 9, 19, 33,  47,  47,   0,   0,   0, 0, 0, 0, ... row n = 3
0, 0, 9, 28, 61, 108, 155, 155,   0,   0, 0, 0, 0, ... row n = 4
0, 0, 0, 28, 89, 197, 352, 507, 507,   0, 0, 0, 0, ... row n = 5
0, 0, 0,  0, 89, 286, 638,1147,1652,1652, 0, 0, 0, ... row n = 6
...
		

References

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

Links

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

Crossrefs

Cf. A052975, A060557, A078038, A095789, A094790

Formula

T(n,n) = A052975(n).

T(n,n+1) = A060557(n).

T(n+1,n) = T(n+2,n) = A094790(n+1).

T(n,n+2) = T(n,n+3) = A094789(n+1).

Sum_{k, 0<=k<=n} T(n-k,k) = (-1)^n*A078038(n).