A147292 Eigentriangle.

1, 1, 1, 2, 1, 2, 5, 2, 2, 5, 13, 5, 4, 5, 14, 34, 13, 10, 10, 14, 41, 89, 34, 26, 25, 28, 41, 122, 233, 89, 68, 65, 70, 82, 122, 365, 610, 233, 178, 170, 182, 205, 244, 365, 1094, 1597, 610, 466, 445, 476, 533, 610, 730, 1094, 3281

Offset: 0

Author

Gary W. Adamson, Nov 05 2008

Keywords

• eigen
• nonn
• tabl

Comments

Left column = odd-indexed Fibonacci numbers prefaced with a 1.

Right border = A007051 shifted.

Row sums are A007051.

Examples

			First few rows of the triangle =
1;
1, 1;
2, 1, 2;
5, 2, 2, 5;
13, 5, 4, 5, 14;
34, 13, 10, 10, 14, 41;
89, 34, 26, 25, 28, 41, 122;
233, 89, 68, 65, 70, 82, 122, 365;
610, 233, 178, 170, 182, 205, 244, 365, 1094;
1597, 610, 466, 445, 476, 533, 610, 730, 1094, 3281;
4181, 1597, 1220, 1665, 1246, 1394, 1586, 1825, 2188, 3281, 9842;
10946, 4181, 3194, 3050, 3262, 3649, 4148, 4745, 5470, 6562, 9842, 29525;
...
Row 4 = (13, 5, 4, 5, 14) = termwise products of (13, 5, 2, 1, 1) and (1, 1, 2, 5, 14).
		

Formula

Let M = an infinite lower triangular matrix with odd-indexed Fibonacci numbers in every column prefaced with a 1: (1, 1, 2, 5, 13, 34, ...). Q = an infinite lower triangular matrix with A007051 prefaced with a 1 as the main diagonal: (1, 1, 2, 5, 14, 41, 122, 365, 1094, ...); and the rest zeros.

A147292 = M * Q