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A216228
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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).
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11
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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
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OFFSET
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0,8
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COMMENTS
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An arithmetic hexagon of E. Lucas.
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REFERENCES
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E. Lucas, Théorie des nombres, Albert Blanchard, Paris 1958, Tome 1, p.89
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LINKS
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FORMULA
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T(n,n+1) = T(n,n+2) = 2^n = A000079(n).
Sum_{k, 0<=k<=n} T(n-k,k) = A016116(n).
Sum_{k, k>=0} T(n,k) = A084215(n+1), n>=1.
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EXAMPLE
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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
...
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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