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A143809 Eigentriangle of the Mobius transform, (A054525). 2
1, -1, 1, -1, 0, 0, 0, -1, 0, -1, -1, 0, 0, 0, -2, 1, -1, 0, 0, 0, -3, -1, 0, 0, 0, 0, 0, -3, 0, 0, 0, 1, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -3, 1, -1, 0, 0, 2, 0, 0, 0, 0, -3, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 1, 0, 3, 0, 0, 0, 0, 0, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 1, -1, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,15

COMMENTS

The eigentriangle of the Mobius transform may be defined by the operation consisting of the termwise product of A054525 row terms and the first n terms of A007554, where A007554: (1, 1, 0, -1, -2, -3, -3,...) = the eigensequence of A054525. A143809 has the following properties:

Sum of n-th row terms = rightmost term of next row.

Right border = A007554, the eigensequence of the Mobius transform.

Row sums = A007554 shifted one place to the left: (1, 0, -1, -2, -3,...).

Left border = mu(n), A008683.

A054525 = the Mobius transform and A007554 = the eigensequence of A054525

First few rows of the triangle = 1;

-1, 1;

-1, 0, 0;

0, -1, 0, -1;

-1, 0, 0, 0, -2;

1, -1, 0, 0, 0, -3;

-1, 0, 0, 0, 0, 0, -3;

0, 0, 0, 1, 0, 0, 0, -4;

0, 0, 0, 0, 0, 0, 0, 0, -3;

1, -1, 0, 0, 2, 0, 0, 0, 0, -3;

...

Example: row 6 = (1, -1, 0, 0, 0, -3) = termwise product of row 6 of the Mobius transform (1, -1, -1, 0, 0, 1) and the first 6 terms of A007554, (the eigensequence of the Mobius transform): (1, 1, 0, -1, -2, -3).

LINKS

Table of n, a(n) for n=1..96.

FORMULA

Triangle read by rows, A054525 * (A007554 * 0^(n-k)); 1<=k<=n

CROSSREFS

A054525, Cf. A008683, A007554

Sequence in context: A209287 A025901 A204431 * A056559 A117200 A107015

Adjacent sequences:  A143806 A143807 A143808 * A143810 A143811 A143812

KEYWORD

tabl,sign

AUTHOR

Gary W. Adamson, Sep 01 2008

STATUS

approved

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Last modified October 17 00:35 EDT 2021. Contains 348048 sequences. (Running on oeis4.)