cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A143468 Triangle read by rows, A054525 * A127775, 1<=k<=n.

Original entry on oeis.org

1, -1, 3, -1, 0, 5, 0, -3, 0, 7, -1, 0, 0, 0, 9, 1, -3, -5, 0, 0, 11, -1, 0, 0, 0, 0, 0, 13, 0, 0, 0, -7, 0, 0, 0, 15, 0, 0, -5, 0, 0, 0, 0, 0, 17, 1, -3, 0, 0, -9, 0, 0, 0, 0, 19, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 21
Offset: 1

Views

Author

Gary W. Adamson, Aug 17 2008

Keywords

Comments

Row sums = A140434: (1, 2, 4, 4, 8, 4, 12, 8, 12,...).
Left border = mu(n), A008683.

Examples

			First few rows of the triangle =
1;
-1, 3;
-1, 0, 5;
0, -3, 0, 7;
-1, 0, 0, 0, 9;
1, -3, -5, 0, 0, 11;
-1, 0, 0, 0, 0, 0, 13;
...

Crossrefs

Cf. A127775, A054525, A140434, A008683.

Formula

Triangle read by rows, A054525 * A127775, 1<=k<=n. Mobius transform of an infinite lower triangular matrix with (1, 3, 5, 7,...) in the main diagonal and the rest zeros.

A144733 Triangle read by rows, 2*A054533 - A054521.

Original entry on oeis.org

1, -3, 2, -3, -3, 4, -1, -4, -1, 4, -3, -3, -3, -3, 8, 1, -2, -4, -2, 1, 4, -3, -3, -3, -3, -3, -3, 12, -1, 0, -1, -8, -1, 0, -1, 8, -1, -1, -6, -1, -1, -6, -1, -1, 12, 1, -2, 1, -2, -8, -2, 1, -2, 1, 8, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, 20
Offset: 1

Views

Author

Gary W. Adamson, Sep 20 2008

Keywords

Comments

Right border = A140434: (1, 2, 4, 4, 8, 4, 12,...).
Left border = A133695: (1, -3, -3, -1, -3, 1, -3, -1,...)
Row sums = A000010, with negative signs after the first 1: (1, -1, -2, -2, -4, -2, -6,...).

Examples

			First few rows of the triangle =
   1;
  -3,  2;
  -3, -3,  4;
  -1, -4, -1,  4;
  -3, -3, -3, -3,  8;
   1, -2, -4, -2,  1,  4;
  -3, -3, -3, -3, -3, -3, 12;
  -1,  0, -1, -8  -1,  0, -1,  8;
  -1, -1, -6, -1, -1, -6, -1, -1, 12;
   1, -2,  1, -2, -8, -2,  1, -2,  1,  8;
  -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, 20;
   ...

Crossrefs

Cf. A000010, A054521, A054532, A054533, A054534, A054535, A140434, A133695.

Formula

Triangle read by rows, 2*A054533 - A054521; as infinite lower triangular matrices.
T(n,k) = -I(gcd(n,k) = 1) + 2 * Sum_{d|gcd(n,k)} d * mu(n/d) for n >= 1 and 1 <= k <= n, where I(condition) = 1 if the condition holds, and 0 otherwise. - Petros Hadjicostas, Jul 29 2019
Previous Showing 11-12 of 12 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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