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

0,2

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,...)

Links

Table of n, a(n) for n=0..54.

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.

Example

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

Sequence in context: A256143 A352791 A274455 * A278425 A309019 A082908

Adjacent sequences: A153276 A153277 A153278 * A153280 A153281 A153282

Keyword

nonn,tabl

Author

Gary W. Adamson, Dec 23 2008

Status

approved