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A103452
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Inverse of number triangle A103451.
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7
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1, -1, 1, -1, 0, 1, -1, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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COMMENTS
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Triangle T(n,k), 0 <= k <= n, read by rows given by [ -1, 2, 0, 0, 0, 0, 0, ...] DELTA [1, 0, -1/2, 1/2, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938. - Philippe Deléham, May 01 2007
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LINKS
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FORMULA
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T(n,k) = 1 if k = n, -1 if k = 0, otherwise 0.
Sum_{k=0..n} T(n, k) = 0^n (row sums).
Sum_{k=0..floor(n/2)} T(n-k, k) = 0^n - (1-(-1)^n)/2 (diagonal sums).
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EXAMPLE
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Triangle begins
1;
-1, 1;
-1, 0, 1;
-1, 0, 0, 1;
-1, 0, 0, 0, 1;
-1, 0, 0, 0, 0, 1;
-1, 0, 0, 0, 0, 0, 1;
-1, 0, 0, 0, 0, 0, 0, 1;
-1, 0, 0, 0, 0, 0, 0, 0, 1;
-1, 0, 0, 0, 0, 0, 0, 0, 0, 1;
-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
Production matrix begins
-1, 1;
-2, 1, 1;
-2, 1, 0, 1;
-2, 1, 0, 0, 1;
-2, 1, 0, 0, 0, 1;
-2, 1, 0, 0, 0, 0, 1;
-2, 1, 0, 0, 0, 0, 0, 1;
-2, 1, 0, 0, 0, 0, 0, 0, 1;
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MATHEMATICA
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Table[Range[n] /. {k_ /; k == 1 && n != 1 -> -1, k_ /; k == n -> 1, _Integer -> 0}, {n, 15}] // Flatten (* Michael De Vlieger, Jul 21 2016 *)
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PROG
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(Sage) flatten([[1 if k==n else -1 if k==0 else 0 for k in (0..n)] for n in (0..15)]) # G. C. Greubel, Jun 18 2021
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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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