A144032 - OEIS

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A144032

Eigentriangle read by rows, T(n,k) = A002321(n-k+1)*A144031(k-1).

1, 0, 1, -1, 0, 1, -1, -1, 0, 0, -2, -1, -1, 0, -2, -1, -2, -1, 0, 0, -6, -2, -1, -2, 0, 2, 0, -10, -2, -2, -1, 0, 2, 6, 0, -13, -2, -2, -2, 0, 46, 10, 0, -10, -1, -2, -2, 0, 2, 12, 10, 13, 0, 4, -2, -1, -2, 0, 4, 6, 10, 13, 10, 0, 36, -2, -2, -1, 0, 4, 12, 10, 26, 10, -4, 0, 84, -3

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

OFFSET

1,11

COMMENTS

Row sums = A144031, the INVERT transform of A002321.

Left border = the Mertens's function, A002321.

Right border = A144031 shifted.

Sum of n-th row terms = rightmost term of (n+1)-th row.

LINKS

Table of n, a(n) for n=1..78.

FORMULA

Eigentriangle read by rows, T(n,k) = A002321(n-k+1)*A144031(k-1).

EXAMPLE

First few rows of the triangle =

0, 1;

-1, 0, 1;

-1, -1, 0, 0;

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

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

-2, -1, -2, 0, 2, 0, -10;

-2, -2, -1, 0, 2, 6, 0, -13;

-2, -2, -2, 0, 4, 6, 10, 0, -10;

...

Row 5 = = (-2, -1, -1, 0, -2) termwise products of (-2, -1, -1, 0, 1) and (1, 1, 1, 0, -2); = ((-2)*1, (-1)*(1), (-1)*(1), (0)*(0), (1)*(-2). (-2, -1, -1, 0, 1) = the first 5 terms of A002321, the Mertens's function.

(1, 1, 1, 0, -2) = 5 shifted terms of A144031.

CROSSREFS

A002321, Cf. A144031.

Sequence in context: A139146 A340489 A277487 * A137686 A341973 A143792

Adjacent sequences: A144029 A144030 A144031 * A144033 A144034 A144035

KEYWORD

tabl,sign

AUTHOR

Gary W. Adamson, Sep 07 2008

STATUS

approved