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A143256 Triangle read by rows, matrix multiplication A051731 * A128407 * A127648, 1<=k<=n. 3
1, 1, -2, 1, 0, -3, 1, -2, 0, 0, 1, 0, 0, 0, -5, 1, -2, -3, 0, 0, 6, 1, 0, 0, 0, 0, 0, -7, 1, -2, 0, 0, 0, 0, 0, 0, 1, 0, -3, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, -5, 0, 0, 0, 0, 10, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11, 1, -2, -3, 0, 0, 6, 0, 0, 0, 0, 0, 0, 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, 14 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Right border = n*mu(n) = A055615.

Row sums = A023900: (1, -1, -2, -1, -4, 2, -6,...).

LINKS

Robert Israel, Table of n, a(n) for n = 1..9870

FORMULA

Triangle read by rows, A051731 * A128407 * A127648, 1<=k<=n

EXAMPLE

First few rows of the triangle =

1;

1, -2;

1, 0, -3;

1, -2, 0, 0;

1, 0, 0, 0, -5;

1, -2, -3, 0, 0, 6;

1, 0, 0, 0, 0, 0, -7;

...

MAPLE

seq(seq(`if`(i mod j = 0, j*numtheory:-mobius(j), 0), j=1..i), i=1..20); # Robert Israel, Sep 07 2014

PROG

(Sage)

A143256_row = lambda n: [k*moebius(k) if k.divides(n) else 0 for k in (1..n)]

for n in (1..10): print(A143256_row(n)) # Peter Luschny, Jan 05 2018

CROSSREFS

Cf. A008683, A055615, A051731, A128407, A127648, A023900.

Sequence in context: A029312 A287352 A243715 * A143151 A130106 A127093

Adjacent sequences:  A143253 A143254 A143255 * A143257 A143258 A143259

KEYWORD

tabl,sign

AUTHOR

Gary W. Adamson, Aug 02 2008

STATUS

approved

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Last modified April 26 09:52 EDT 2019. Contains 322472 sequences. (Running on oeis4.)