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A152904
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Triangle read by rows: T(n,k) = A008683(n-k+1); 1<=k<=n; mu(n) "decrescendo".
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1
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1, -1, 1, -1, -1, 1, 0, -1, -1, 1, -1, 0, -1, -1, 1, 1, -1, 0, -1, -1, 1, -1, 1, -1, 0, -1, -1, 1, 0, -1, 1, -1, 0, -1, -1, 1, 0, 0, -1, 1, -1, 0, -1, -1, 1, 1, 0, 0, -1, 1, -1, 0, -1, -1, 1, -1, 1, 0, 0, -1, 1, -1, 0, -1, -1, 1
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OFFSET
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1,1
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LINKS
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E. Deutsch, L. Ferrari and S. Rinaldi, Production Matrices, Advances in Applied Mathematics, 34 (2005) pp. 101-122.
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FORMULA
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Triangle read by rows, T(n,k) = A008683(n-k+1) = A008683 in every column = A008683 "decrescendo"d by rows.
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EXAMPLE
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Triangle begins
1;
-1, 1;
-1, -1, 1;
0, -1, -1, 1;
-1, 0, -1, -1, 1;
1, -1, 0, -1, -1, 1;
-1, 1, -1, 0, -1, -1, 1;
0, -1, 1, -1, 0, -1, -1, 1;
0, 0, -1, 1, -1, 0, -1, -1, 1;
...
Production matrix begins
-1, 1,
-2, 0, 1,
-3, 0, 0, 1,
-6, 0, 0, 0, 1,
-9, 0, 0, 0, 0, 1,
-17, 0, 0, 0, 0, 0, 1,
-28, 0, 0, 0, 0, 0, 0, 1,
-50, 0, 0, 0, 0, 0, 0, 0, 1,
-83, 0, 0, 0, 0, 0, 0, 0, 0, 1,
-147, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ...
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CROSSREFS
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Row sums = A002321, the Mertens function. A185694 is an eigensequence.
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KEYWORD
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AUTHOR
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STATUS
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approved
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