A144824 - OEIS

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A144824

Triangle read by rows, A054533 * A127648 (matrix product).

1, -1, 2, -1, -2, 6, 0, -4, 0, 8, -1, -2, -3, -4, 20, 1, -2, -6, -4, 5, 12, -1, -2, -3, -4, -5, -6, 42, 0, 0, 0, -16, 0, 0, 0, 32, 0, 0, -9, 0, 0, -18, 0, 0, 54, 1, -2, 3, -4, -20, -6, 7, -8, 9, 40, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, 110

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

Row sums = A023896: (1, 1, 3, 4, 10, 16, 21, ...).

Right border = A002618: (1, 2, 6, 8, 20, 12, ...).

Left border = mu(n) = A008683 (n).

LINKS

Jinyuan Wang, Table of n, a(n) for n = 1..10000

FORMULA

Triangle read by rows, A054533 * A127648 (matrix product). The operation is equivalent to taking termwise products of row A054533 terms and the natural numbers.

T(n, k) = k * Sum_{d|gcd(n,k)} d * mu(n/d) for n >= 1 and 1 <= k <= n. - Petros Hadjicostas, Jul 28 2019

a(n) = A002260(n)*A054533(n). - Jinyuan Wang, Jul 29 2019

EXAMPLE

Triangle A054533 starts as follows:

-1, 1;

-1, -1, 2;

0, -2, 0, 2;

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

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

...

The first few rows of triangle A144824 are as follows:

-1, 2;

-1, -2, 6;

0, -4, 0, 8;

-1, -2, -3, -4, 20;

1, -2, -6, -4, 5, 12;

-1, -2, -3, -4, -5, -6, 42;

...

CROSSREFS

Cf. A002260, A002618, A008683, A023896, A054533, A127648.

Sequence in context: A032238 A000619 A006602 * A364513 A144358 A049404

Adjacent sequences: A144821 A144822 A144823 * A144825 A144826 A144827

KEYWORD

tabl,sign

AUTHOR

Gary W. Adamson, Sep 21 2008

STATUS

approved