A158948 -id:A158948 - cp's OEIS frontend

A158951 Triangle read by rows, A051731 * A158948.

1, 2, 1, 3, 0, 1, 4, 2, 0, 1, 4, 0, 1, 0, 1, 7, 2, 1, 1, 0, 1, 5, 0, 1, 0, 1, 0, 1, 8, 3, 0, 2, 0, 1, 0, 18, 0, 2, 0, 1, 0, 1, 0, 1, 10, 2, 1, 1, 1, 1, 0, 1, 0, 1

Offset: 1

Gary W. Adamson & Mats Granvik, Mar 31 2009

Row sums = sigma(n), A000203. Left column = A079247

			First few rows of the triangle =
1;
2, 1;
3, 0, 1;
4, 2, 0, 1;
4, 0, 1, 0, 1;
7, 2, 1, 1, 0, 1;
5, 0, 1, 0, 1, 0, 1;
8, 3, 0, 2, 0, 1, 0, 1;
8, 0, 2, 0, 1, 0, 1, 0, 1;
10, 2, 1, 1, 1, 1, 0, 1, 0, 1;
7, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1;
15, 4, 1, 3, 0, 2, 0, 10, 1, 0, 1;
8, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1;
13, 2, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1;
...

Cf. A158948, A000203, A051731

Triangle read by rows, A051731 * A158948

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).

Original entry on oeis.org

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

Gary W. Adamson, Mar 31 2009

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.

			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.

A158948, A000071

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;...).

cp's OEIS Frontend

A158951 Triangle read by rows, A051731 * A158948.

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