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A216238
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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).
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5
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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
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OFFSET
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0,8
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COMMENTS
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Hexagon arithmetic of E. Lucas.
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REFERENCES
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E. Lucas, Théorie des nombres, Albert Blanchard, Paris, 1958, Tome1, p.89
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LINKS
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FORMULA
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T(n,n+3) = T(n,n+4) = A003462(n+1).
Sum_{k, 0<=k<=n} T(n-k,k) = A182522(n).
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EXAMPLE
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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
...
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CROSSREFS
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Similar sequences: A216201, A216210, A216216, A216218, A216219, A216220, A216226, A216228, A216229, A216230, A216232, A216235, A216236.
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KEYWORD
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AUTHOR
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STATUS
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approved
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