

A153279


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


3



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
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OFFSET

0,2


COMMENTS

Row sums = 3^n
Sum of nth 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(nk); 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: A090278 A256143 A274455 * A278425 A309019 A082908
Adjacent sequences: A153276 A153277 A153278 * A153280 A153281 A153282


KEYWORD

nonn,tabl


AUTHOR

Gary W. Adamson, Dec 23 2008


STATUS

approved



