A145580 Eigentriangle, row sums = A000930

1, 1, 1, 0, 1, 2, -1, 0, 2, 3, 0, -1, 0, 3, 4, 1, 0, -2, 0, 4, 6, 0, 1, 0, -3, 0, 6, 9, -1, 0, 2, 0, -4, 0, 9, 13, 0, -1, 0, 3, 0, -6, 0, 13, 19, 1, 0, -2, 0, 4, 0, -9, 0, 19, 28

Offset

1,6

Comments

Row sums = A000930 starting with offset 1: (1, 1, 2, 3, 4, 6, 9, 13, 19,...).

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

Links

Table of n, a(n) for n=1..55.

Formula

Let M = an infinite lower triangular matrix with (1, 1, 0, -1, 0, 1, 0, -1, 0, 1,...) in every column; and X = an infinite lower triangular matrix with A000930 as the main diagonal (offset 1): (1, 1, 2, 3, 4, 6, 9, 13, 19,...) and the rest zeros. Triangle A145580 = M * X.

Example

First few rows of the triangle =
1;
1, 1;
0, 1, 2;
-1, 0, 2, 3;
0, -1, 0, 3, 4;
1, 0, -2, 0, 4, 6;
0, 1, 0, -3, 0, 6, 9;
-1, 0, 2, 0, -4, 0, 9, 13;
0, -1, 0, 3, 0, -6, 0, 13, 19;
1, 0, -2, 0, 4, 0, -9, 0, 19, 28;
...
Row 6 = (1, 0, -2, 0, 4, 6) = termwise products of (1, 0, -1, 0, 1, 1) and (1, 1, 2, 3, 4, 6).

Crossrefs

A000930

Sequence in context: A308321 A097854 A161515 * A144219 A144027 A019591

Adjacent sequences: A145577 A145578 A145579 * A145581 A145582 A145583

Keyword

tabl,sign

Author

Gary W. Adamson, Oct 13 2008

Status

approved