A214846 Square array T, read by antidiagonals: T(n,k) = 0 if n-k >= 6 or if k-n >= 6, T(k,0) = T(0,k) = 1 if 0 <= k <= 5, T(n,k) = T(n-1,k) + T(n,k-1).

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 5, 10, 10, 5, 1, 0, 6, 15, 20, 15, 6, 0, 0, 6, 21, 35, 35, 21, 6, 0, 0, 0, 27, 56, 70, 56, 27, 0, 0, 0, 0, 27, 83, 126, 126, 83, 27, 0, 0, 0, 0, 0, 110, 209, 252, 209, 110, 0, 0, 0, 0, 0, 0, 110, 319, 461, 461, 319, 110, 0, 0, 0, 0, 0, 0, 0, 429, 780, 922, 780, 429, 0, 0, 0, 0

Offset: 0

Author

Philippe Deléham, Mar 16 2013

Keywords

• nonn
• tabl

Comments

An arithmetic hexagon of E. Lucas.

Examples

			Square array begins:
  1, 1,  1,   1,   1,   1,    0,    0,    0,     0,     0, ...
  1, 2,  3,   4,   5,   6,    6,    0,    0,     0,     0, ...
  1, 3,  6,  10,  15,  21,   27,   27,    0,     0,     0, ...
  1, 4, 10,  20,  35,  56,   83,  110,  110,     0,     0, ...
  1, 5, 15,  35,  70, 126,  209,  319,  429,   429,     0, ...
  1, 6, 21,  56, 126, 252,  461,  780, 1209,  1638,  1638, ...
  0, 6, 27,  83, 209, 461,  922, 1702, 2911,  4549,  6187, ...
  0, 0, 27, 110, 319, 780, 1702, 3404, 6315, 10864, 17051, ...
  ...
		

Links

• E. Lucas, Théorie des nombres, Gauthier-Villars, Paris 1891, Tome 1, p. 89.

Crossrefs

Cf. similar sequences: A000007, A216218, A216216, A216210, A216219.

Formula

T(n,n) = A087944(n).

T(n,n+1) = T(n+1,n) = A087946(n).

T(n+2,n) = T(n,n+2) = A001353(n+1).

T(n+3,n) = T(n,n+3) = A216271(n).

T(n+5,n) = T(n+4,n) = T(n,n+4) = T(n,n+5) = A216263(n).

Sum_{k=0..n} T(n-k,k) = A216241(n).