A153279 Eigentriangle by rows, T(n,k) = A000079(n-k) * (diagonalized matrix of (1,1,3,9,27,81,...)).

1, 2, 1, 4, 2, 3, 8, 4, 6, 9, 16, 8, 12, 18, 27, 32, 16, 24, 36, 54, 81, 64, 32, 48, 72, 108, 162, 243, 128, 64, 96, 144, 216, 324, 486, 729, 256, 128, 192, 288, 432, 648, 972, 1458, 2187, 512, 256, 384, 576, 864, 1296, 1944, 2916, 4374, 6561

Offset: 0

Author

Gary W. Adamson, Dec 23 2008

Keywords

• nonn
• tabl

Comments

Row sums = 3^n

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

Eigensequence of the triangle = A153280: (1, 3, 15, 165, 4785, 397155,...)

Examples

			First few rows of the triangle =
1;
2, 1;
4, 2, 3;
8, 4, 6, 9;
16, 8, 12, 18, 27;
32, 16, 24, 36, 54, 81;
64, 32, 48, 72, 108, 162, 243;
128, 64, 96, 144, 216, 324, 486, 729;
256, 128, 192, 288, 432, 648, 972, 1458, 2187;
512, 256, 384, 576, 864, 1296, 1944, 2916, 4374, 6561;
...
Row 3 = (8, 4, 6, 9) = termwise products of (8, 4, 2, 1) and (1, 1, 3, 9).
		

Crossrefs

Cf. A000079, A000244, A153280

Formula

Triangle read by rows, M*Q. M = triangle T(n,k) = A000079(n-k); powers of 2 in every column. Q = an infinite lower triangular matrix with powers of 3 prefaced with a 1: (1,1,3,9,27,...) as the main diagonal and the rest zeros.