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

%I

%S 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,

%T 162,243,128,64,96,144,216,324,486,729,256,128,192,288,432,648,972,

%U 1458,2187,512,256,384,576,864,1296,1944,2916,4374,6561

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

%C Row sums = 3^n

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

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

%F 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.

%e First few rows of the triangle =

%e 1;

%e 2, 1;

%e 4, 2, 3;

%e 8, 4, 6, 9;

%e 16, 8, 12, 18, 27;

%e 32, 16, 24, 36, 54, 81;

%e 64, 32, 48, 72, 108, 162, 243;

%e 128, 64, 96, 144, 216, 324, 486, 729;

%e 256, 128, 192, 288, 432, 648, 972, 1458, 2187;

%e 512, 256, 384, 576, 864, 1296, 1944, 2916, 4374, 6561;

%e ...

%e Row 3 = (8, 4, 6, 9) = termwise products of (8, 4, 2, 1) and (1, 1, 3, 9).

%Y Cf. A000079, A000244, A153280

%K nonn,tabl

%O 0,2

%A _Gary W. Adamson_, Dec 23 2008

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Last modified June 19 21:04 EDT 2021. Contains 345147 sequences. (Running on oeis4.)