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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| 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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FORMULA
| 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
| 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
| Cf. A008683, A097945, A020639, A054525.
Sequence in context: A187616 A050464 A014405 * A127448 A128179 A178780
Adjacent sequences: A143150 A143151 A143152 * A143154 A143155 A143156
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KEYWORD
| tabl,sign
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AUTHOR
| Gary W. Adamson & Mats O. Granvik (qntmpkt(AT)yahoo.com), Jul 27 2008
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