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A217593
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Square array T, read by antidiagonals: T(n,k) = 0 if n-k >=1 or if k-n >= 9, T(0,k) = 1 for k = 0..8, T(n,k) = T(n-1,k) + T(n,k-1).
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3
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1, 1, 0, 1, 1, 0, 1, 2, 0, 0, 1, 3, 2, 0, 0, 1, 4, 5, 0, 0, 0, 1, 5, 9, 5, 0, 0, 0, 1, 6, 14, 14, 0, 0, 0, 0, 1, 7, 20, 28, 14, 0, 0, 0, 0, 0, 8, 27, 48, 42, 0, 0, 0, 0, 0, 0, 8, 35, 75, 90, 42, 0, 0, 0, 0, 0, 0, 0, 43, 110, 165, 132, 0, 0, 0, 0, 0, 0, 0, 0, 43, 153, 275, 297, 132, 0, 0, 0, 0, 0, 0, 0, 0, 0, 196, 428, 572, 429, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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0,8
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REFERENCES
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A hexagon arithmetic of E. Lucas.
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LINKS
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FORMULA
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T(n,n+7) = T(n,n+8) = A094865(n+3).
Sum_{k, 0<=k<=n} T(n-k,k) = A178381(n).
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EXAMPLE
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Square array begins :
1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, ...
0, 1, 2, 3, 4, 5, 6, 7, 8, 8, 0, 0, ...
0, 0, 2, 5, 9, 14, 20, 27, 35, 43, 43, 0, 0, ...
0, 0, 0, 5, 14, 28, 75, 110, 153, 196, 196, 0, 0, ....
0, 0, 0, 0, 14, 42, 90, 165, 275, 428, 624, 820, 820, 0, 0, ...
...
Square array, read by rows, with 0 omitted:
1, 1, 1, 1, 1, 1, 1, 1, 1
1, 2, 3, 4, 5, 6, 7, 8, 8
2, 5, 9, 14, 20, 27, 35, 43, 43
5, 14, 28, 48, 75, 110, 153, 196, 196
14, 42, 90, 165, 275, 428, 624, 820, 820
42, 132, 297, 572, 1000, 1624, 2444, 3264, 3264
132, 429, 1001, 2001, 3625, 6069, 9333, 12597, 12597
429, 1430, 3431, 7056, 13125, 22458, 35055, 47652, 47652
...
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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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