A124732 -id:A124732 - cp's OEIS frontend

A124730 Triangle, row sums = powers of 3.

1, 1, 2, 1, 6, 2, 1, 14, 8, 4, 1, 30, 22, 24, 4, 1, 62, 52, 92, 28, 8, 1, 126, 114, 288, 120, 72, 8, 1, 254, 240, 804, 408, 384, 80, 16, 1, 510, 494, 2088, 1212, 1584, 46, 192, 16

Offset: 0

Gary W. Adamson & Roger L. Bagula, Nov 05 2006

In A124731, we switch the diagonals. In both triangles, row sums = powers of 3.

			Row 2 = (1, 6, 2) since [1,0,0; 2,2,0; 0,1,1]^2 * [1,0,0] = [1,6,2].
First few rows of the triangle are:
1;
1, 2;
1, 6, 2;
1, 14, 8, 4;
1, 30, 22, 24, 4;
1, 62, 52, 92, 28, 8;
1, 126, 114, 288, 120, 72, 8;
...

Cf. A124731, A124732.

Let M = the infinite bidiagonal matrix with (1,2,1,2...) in the main diagonal and (2,1,2,1...) in the subdiagonal. The n-th row of the triangle (extracting the zeros) = M^n * [1,0,0,0...].

A124731 Triangle, row sums = powers of 3, companion to A124730.

Original entry on oeis.org

1, 2, 1, 4, 3, 2, 8, 7, 10, 2, 16, 15, 34, 12, 4, 32, 31, 98, 46, 32, 4, 64, 63, 258, 144, 156, 36, 8, 128, 127, 642, 402, 600, 192, 88, 8, 256, 255, 1538, 1044, 2004, 792, 560, 96, 16

Offset: 0

Gary W. Adamson & Roger L. Bagula, Nov 05 2006

In A124730, the diagonals are switched. Row sums are powers of 3 in both triangles.

			Row 2 = (4, 3, 2) since (using the 3 X 3 matrix m = [2,0,0; 1,1,0; 0,2,2]), m^2 * [1,0,0] = [4,3,2].
First few rows of the triangle are:
1;
2, 1;
4, 3, 2;
8, 7, 10, 2;
16, 15, 34, 12, 4;
32, 31, 98, 46, 32, 4;
64, 63, 258, 144, 156, 36, 8;
...

Cf. A124730, A124732.

Let M = the infinite bidiagonal matrix with (2,1,2,1...) in the main diagonal and (1,2,1,2...) in the subdiagonal. Extracting finite n X n matrices of this form, we take M^n * [1,0,0,0...].

cp's OEIS Frontend

A124730 Triangle, row sums = powers of 3.

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