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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).
5
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
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
...
KEYWORD
nonn,tabl
AUTHOR
Philippe Deléham, Mar 14 2013
STATUS
approved