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A214846
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Square array T, read by antidiagonals: T(n,k) = 0 if n-k >= 6 or if k-n >= 6, T(k,0) = T(0,k) = 1 if 0 <= k <= 5, T(n,k) = T(n-1,k) + T(n,k-1).
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5
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1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 5, 10, 10, 5, 1, 0, 6, 15, 20, 15, 6, 0, 0, 6, 21, 35, 35, 21, 6, 0, 0, 0, 27, 56, 70, 56, 27, 0, 0, 0, 0, 27, 83, 126, 126, 83, 27, 0, 0, 0, 0, 0, 110, 209, 252, 209, 110, 0, 0, 0, 0, 0, 0, 110, 319, 461, 461, 319, 110, 0, 0, 0, 0, 0, 0, 0, 429, 780, 922, 780, 429, 0, 0, 0, 0
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OFFSET
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0,5
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COMMENTS
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An arithmetic hexagon of E. Lucas.
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LINKS
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FORMULA
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T(n+2,n) = T(n,n+2) = A001353(n+1).
T(n+5,n) = T(n+4,n) = T(n,n+4) = T(n,n+5) = A216263(n).
Sum_{k=0..n} T(n-k,k) = A216241(n).
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EXAMPLE
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Square array begins:
1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, ...
1, 2, 3, 4, 5, 6, 6, 0, 0, 0, 0, ...
1, 3, 6, 10, 15, 21, 27, 27, 0, 0, 0, ...
1, 4, 10, 20, 35, 56, 83, 110, 110, 0, 0, ...
1, 5, 15, 35, 70, 126, 209, 319, 429, 429, 0, ...
1, 6, 21, 56, 126, 252, 461, 780, 1209, 1638, 1638, ...
0, 6, 27, 83, 209, 461, 922, 1702, 2911, 4549, 6187, ...
0, 0, 27, 110, 319, 780, 1702, 3404, 6315, 10864, 17051, ...
...
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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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