1,2

A163313 is an eigentriangle (i.e. a lower triangular matrix * a diagonalized

version of its eigensequence); A014668 is the eigensequence of triangle A010766.

Row sums = A014668 starting (1, 3, 7, 16, 33, 71, 143,...).

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

Equls M * Q as infinite lower triangular matrices, where M = triangle A010766 and Q = a matrix with A014668: (1, 1, 3, 7, 16, 33, 71, 143,...) as the main diagonal and the rest zeros.

First few rows of the triangle =

1;

2, 1;

3, 1, 3;

4, 2, 3, 7;

5, 2, 3, 7, 16;

6, 3, 6, 7, 16, 33;

7, 3, 6, 7, 16, 33 71;

8, 4, 6, 14, 16, 33, 71, 143;

9, 4, 9, 14, 16, 33, 71, 143, 295;

10, 5, 9, 14, 32, 33, 71, 143, 295, 594;

11, 5, 9, 14, 32, 33, 71, 143, 295, 594, 1206;

12, 6, 12, 21, 32, 66, 71, 143, 295, 594, 1206, 2413;

...

Example: row 4 = (4, 2, 3, 7) = (4, 2, 1, 1) * (1, 1, 3, 7).

A010766, A014668

Sequence in context: A050123 A081386 A143802 this_sequence A135591 A114897 A123539

Adjacent sequences: A163310 A163311 A163312 this_sequence A163314 A163315 A163316

nonn,tabl

Gary W. Adamson & Mats Granvik (qntmpkt(AT)yahoo.com), Jul 30 2009