A216238 Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=1 or if k-n>=5, T(0,0) = T(0,1) = T(0,2) = T(0,3) = T(0,4) = 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, 0, 4, 5, 0, 0, 0, 0, 4, 9, 5, 0, 0, 0, 0, 0, 13, 14, 0, 0, 0, 0, 0, 0, 13, 27, 14, 0, 0, 0, 0, 0, 0, 0, 40, 41, 0, 0, 0, 0, 0, 0, 0, 0, 40, 81, 41, 0, 0, 0, 0, 0, 0, 0, 0, 0, 121, 122, 0, 0, 0, 0, 0, 0

Offset

0,8

Comments

Hexagon arithmetic of E. Lucas.

References

E. Lucas, Théorie des nombres, Albert Blanchard, Paris, 1958, Tome1, p.89

Links

Table of n, a(n) for n=0..77.

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

Formula

T(n,n) = A124302(n).

T(n,n+1) = A124302(n+1).

T(n,n+2) = 3^n = A000244(n).

T(n,n+3) = T(n,n+4) = A003462(n+1).

Sum_{k, 0<=k<=n} T(n-k,k) = A182522(n).

Example

Square array begins:
1, 1, 1, 1,  1,  0,   0,   0,   0,    0,    0, ... row n=0
0, 1, 2, 3,  4,  4,   0,   0,   0,    0,    0, ... row n=1
0, 0, 2, 5,  9, 13,  13,   0,   0,    0,    0, ... row n=2
0, 0, 0, 5, 14, 27,  40,  40,   0,    0,    0, ... row n=3
0, 0, 0, 0, 14, 41,  81, 121, 121,    0,    0, ... row n=4
0, 0, 0, 0,  0, 41, 122, 243, 364,  364,    0, ... row n=5
0, 0, 0, 0,  0,  0, 122, 365, 729, 1093, 1093, ... row n=6
...

Crossrefs

Cf. A000244, A003462, A124302, A182522.

Similar sequences: A216201, A216210, A216216, A216218, A216219, A216220, A216226, A216228, A216229, A216230, A216232, A216235, A216236.

Sequence in context: A332898 A175045 A292377 * A157608 A220062 A216054

Adjacent sequences: A216235 A216236 A216237 * A216239 A216240 A216241

Keyword

nonn,tabl

Author

Philippe Deléham, Mar 14 2013

Status

approved