A217257 Square array T, read by antidiagonals: T(n,k) = 0 if n-k >= 1 or if k-n >= 7, T(0,0) = T(0,1) = T(0,2) = T(0,3) = T(0,3) = T(0,4) = T(0,5) = T(0,6) = 1, T(n,k) = T(n-1,k) + T(n,k-1).

1, 1, 0, 1, 1, 0, 1, 2, 0, 0, 1, 3, 2, 0, 0, 1, 4, 5, 0, 0, 0, 1, 5, 9, 5, 0, 0, 0, 0, 6, 14, 14, 0, 0, 0, 0, 0, 6, 20, 28, 14, 0, 0, 0, 0, 0, 0, 26, 48, 42, 0, 0, 0, 0, 0, 0, 0, 26, 74, 90, 42, 0, 0, 0, 0, 0, 0, 0, 0, 100, 164, 132, 0, 0, 0, 0, 0, 0, 0, 0, 0, 100, 264, 296, 132, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 364, 560, 428, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Author

Philippe Deléham, Mar 17 2013

Keywords

• nonn
• tabl

Comments

A hexagon arithmetic of E. Lucas.

Examples

			Square array begins:
1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... row n=0
0, 1, 2, 3, 4, 5, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... row n=1
0, 0, 2, 5, 9, 14, 20, 26, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... row n=2
0, 0, 0, 5, 14, 28, 48, 74, 100, 100, 0, 0, 0, 0, 0, 0, 0, ... row n=3
0, 0, 0, 0, 14, 42, 90, 162, 264, 364, 364, 0, 0, 0, 0, 0, ... row n=4
0, 0, 0, 0, 0, 42, 132, 296, 560, 924, 1288, 1288, 0, 0, 0, ... row n=5
...
		

References

• E. Lucas, Théorie des nombres, A. Blanchard, Paris, 1958, p.89

Links

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

Crossrefs

Cf. similar sequences: A216230, A216228, A216226, A216238, A216054.

Formula

T(n,n) = A024175(n).

T(n,n+1) = A024175(n+1).

T(n,n+2) = A094803(n+1).

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

T(n,n+4) = A094806(n+2).

T(n,n+5) = T(n,n+6) = A094811(n+2).

Sum_{k, 0<=k<=n} T(n-k,k) = A030436(n).

Extensions

a(69) = 0 deleted by Georg Fischer, Oct 16 2021