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A143153
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Triangle read by rows, A054525 * (A020639 * 0^(n-k)), 1<=k<=n.
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1
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1, -1, 2, -1, 0, 3, 0, -2, 0, 2, -1, 0, 0, 0, 5, 1, -2, -3, 0, 0, 2, -1, 0, 0, 0, 0, 0, 7, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, -3, 0, 0, 0, 0, 0, 3, 1, -2, 0, 0, -5, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 2, 0, -2, 0, -2, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 1, -2, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 0, 2
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OFFSET
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1,3
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COMMENTS
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Right border = A020639, Lpf(n): (1, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11,...).
Left border = mu(n), A008683: (1, -1, -1, 0, -1, 1, -1,...).
Row sums = a signed version of A097945: (1, -1, -2, 0, -4, 2, -6,...) such that parity = (+) iff mu(n) = +.
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LINKS
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FORMULA
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Triangle read by rows, A054525 * (A020639 * 0^(n-k)), 1<=k<=n; where A020639 = Lpf(n): (1, 2, 3, 2, 5, 2, 7, 2, 3, 2,...) and A054525 = the Mobius transform.
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EXAMPLE
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First few rows of the triangle =
1;
-1, 2;
-1, 0, 3;
0, -2, 0, 2;
-1, 0, 0, 0, 5;
1, -2, -3, 0, 0, 2;
-1, 0, 0, 0, 0, 0, 7;
0, 0, 0, -2, 0, 0, 0, 2;
0, 0, -3, 0, 0, 0, 0, 0, 3;
1, -2, 0, 0, -5, 0, 0, 0, 0, 2;
-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11;
0, 2, 0, -2, 0, -2, 0, 0, 0, 0, 0, 2;
...
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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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