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

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 =
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, 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