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

0,3

Comments

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

Links

Table of n, a(n) for n=0..44.

Formula

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...].

Example

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;
...

Crossrefs

Cf. A124731, A124732.

Sequence in context: A133200 A103881 A101024 * A114283 A106187 A110135

Adjacent sequences: A124727 A124728 A124729 * A124731 A124732 A124733

Keyword

nonn,tabl

Author

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

Status

approved