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A257564
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Irregular triangle read by rows: T(n,k) = r(n+k)+r(n-k) with r(n) = (n-(n mod 2))/2 for n>=0 and -n<=k<=n.
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2
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0, 1, 0, 1, 2, 1, 2, 1, 2, 3, 2, 3, 2, 3, 2, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8
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refs;
listen;
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text;
internal format)
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OFFSET
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0,5
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COMMENTS
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r(n+k)-r(n-k) is triangle A196199(n,k).
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LINKS
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FORMULA
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Sum_{k=-n..n} T(n,k) = 2*n^2 = A001105(n).
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EXAMPLE
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Triangle starts:
0;
1, 0, 1;
2, 1, 2, 1, 2;
3, 2, 3, 2, 3, 2, 3;
4, 3, 4, 3, 4, 3, 4, 3, 4;
5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5;
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MAPLE
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r := n -> (n-(n mod 2))/2: T := (n, k) -> r(n+k) + r(n-k):
seq(print(seq(T(n, k), k=-n..n)), n=0..6);
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PROG
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(Sage)
for n in (0..6):
[(n+k)//2 + (n-k)//2 for k in (-n..n)]
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CROSSREFS
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KEYWORD
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tabf,easy,nonn
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AUTHOR
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STATUS
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approved
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