A158950 Triangle read by rows, A158948 * (an infinite lower triangular matrix with A000071 prefaced with a 1 as the right border; and the rest zeros).

1, 1, 1, 2, 0, 2, 2, 1, 0, 4, 3, 0, 2, 0, 7, 3, 1, 0, 4, 0, 12, 4, 0, 2, 0, 7, 0, 20, 4, 1, 0, 4, 0, 12, 0, 33, 5, 0, 2, 0, 7, 0, 20, 0, 54, 5, 1, 0, 4, 0, 12, 0, 33, 0, 88, 6, 0, 2, 0, 7, 0, 20, 0, 54, 0, 143

Offset

1,4

Comments

Row sums = A000071 starting with nonzero terms: (1, 2, 4, 7, 12,...) As a property of eigentriangles, sum of n-th row terms = rightmost term of next row.

Links

Table of n, a(n) for n=1..66.

Formula

Triangle read by rows, A158948 * M; where M = (an infinite lower triangular matrix with A000071 prefaced with a 1 as the right border, and the rest zeros). M = (1; 0,1; 0,0,2; 0,0,0,4; 0,0,0,7;...).

Example

First few rows of the triangle =
1;
1, 1;
2, 0, 2;
2, 1, 0, 4;
3, 0, 2, 0, 7;
3, 1, 0, 4, 0, 12;
4, 0, 2, 0, 7, 0, 20;
4, 1, 0, 4, 0, 12, 0, 33;
5, 0, 2, 0, 7, 0, 20, 0, 54;
5, 1, 0, 4, 0, 12, 0, 33, 0, 88;
6, 0, 2, 0, 7, 0, 20, 0, 54, 0, 143;
6, 1, 0, 4, 0, 12, 0, 33, 0, 88, 0, 232;
7, 0, 2, 0, 7, 0, 20, 0, 54, 0, 143, 0, 376;
7, 1, 0, 4, 0, 12, 0, 33, 0, 88, 0, 232, 0, 609;
...
Row 4 = (2, 1, 0, 4) = termwise products of (2, 1, 0, 1) and (1, 1, 2, 4);
where (2, 1, 0, 1) = row 4 of triangle A158948, and (1, 1, 2, 4) = the 3 nonzero terms of A000071 prefaced with a 1.

Crossrefs

A158948, A000071

Sequence in context: A058728 A143751 A353322 * A213013 A242667 A059581

Adjacent sequences: A158947 A158948 A158949 * A158951 A158952 A158953

Keyword

eigen,nonn,tabl

Author

Gary W. Adamson, Mar 31 2009

Status

approved