A145579 Eigentriangle, row sums = A001590

1, 1, 1, 0, 1, 2, 1, 0, 2, 3, 1, 1, 0, 3, 6, 0, 1, 2, 0, 6, 11, 1, 0, 2, 3, 0, 11, 20, 1, 1, 0, 3, 6, 0, 20, 37, 0, 1, 2, 0, 6, 11, 0, 37, 68, 1, 0, 2, 3, 0, 11, 20, 0, 68, 125

Offset

3,6

Comments

Row sums = A001590 starting (1, 2, 3, 6, 11, 20, 37,...).

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

Links

Table of n, a(n) for n=3..57.

Formula

Let M = an infinite lower triangular matrix with (1, 1, 0, 1, 1, 0,...) in every column and X = a diagonalized matrix of A001590: (1, 1, 2, 3, 6, 11, 20, 37,...), (i.e. A001590 starting with offset 3 as a diagonal prefaced with a 1; and the rest zeros). Triangle A145579 = M * X.

Example

First few rows of the triangle =
1;
1, 1;
0, 1, 2;
1, 0, 2, 3;
1, 1, 0, 3, 6;
0, 1, 2, 0, 6, 11;
1, 0, 2, 3, 0, 11, 20;
1, 1, 0, 3, 6, 0, 20, 37;
0, 1, 2, 0, 6, 11, 0, 37, 68;
1, 0, 2, 3, 0, 11, 20, 0, 68, 125;
...
Row 7 = (1, 1, 0, 3, 6) = termwise products of (1, 1, 0, 1, 1) and (1, 1, 2, 3, 6).

Crossrefs

A001590

Sequence in context: A123949 A236358 A144082 * A167655 A346148 A262781

Adjacent sequences: A145576 A145577 A145578 * A145580 A145581 A145582

Keyword

nonn,tabl

Author

Gary W. Adamson, Oct 13 2008

Extensions

Alignment of example rows and unintentional concatenation of values fixed by Charles J. Daniels (chajadan(AT)gmail.com), Dec 05 2009

Status

approved