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A216228
Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=1 or if k-n>=3, T(0,0) = T(0,1) = T(0,2) = 1, T(n,k) = T(n-1,k) + T(n,k-1).
11
1, 1, 0, 1, 1, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 32
OFFSET
0,8
COMMENTS
An arithmetic hexagon of E. Lucas.
REFERENCES
E. Lucas, Théorie des nombres, Albert Blanchard, Paris 1958, Tome 1, p.89
LINKS
E. Lucas, Théorie des nombres, Tome 1, Jacques Gabay, Paris, 1991, p.89
FORMULA
T(n,n) = A011782(n).
T(n,n+1) = T(n,n+2) = 2^n = A000079(n).
Sum_{k, 0<=k<=n} T(n-k,k) = A016116(n).
Sum_{n, n>=0} T(n,k) = A084215(k).
Sum_{k, k>=0} T(n,k) = A084215(n+1), n>=1.
EXAMPLE
Square array begins:
1, 1, 1, 0, 0, 0, 0, 0, ... row n=0
0, 1, 2, 2, 0, 0, 0, 0, ... row n=1
0, 0, 2, 4, 4, 0, 0, 0, ... row n=2
0, 0, 0, 4, 8, 8, 0, 0, ... row n=3
0, 0, 0, 0, 8, 16, 16, 0, ... row n=4
0, 0, 0, 0, 0, 16, 32, 32, ... row n=5
...
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Philippe Deléham, Mar 13 2013
STATUS
approved