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Eigentriangle, row sums = number of ordered partitions of n into powers of 2
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%I #11 Sep 13 2023 09:17:31

%S 1,1,1,0,1,2,1,0,2,3,0,1,0,3,6,0,0,2,0,6,10,0,0,0,3,0,10,18,1,0,0,0,6,

%T 0,18,31,0,1,0,0,0,10,0,31,56,0,0,2,0,0,0,18,0,56,98,0,0,0,3,0,0,0,31,

%U 0,98,174,0,0,0,0,6,0,0,0,56,0,174,306,0,0,0,0,0,10,0,0,98,0,306,542,0,0

%N Eigentriangle, row sums = number of ordered partitions of n into powers of 2

%C Right border of the triangle = A023359: (1, 1, 2, 3, 6, 10, 18,...) the number of ordered partitions of n into powers of 2.

%C Row sums = A023359 starting with offset 1: (1, 2, 3, 6, 10, 18,...).

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

%F Equals A*B, where A = an infinite lower triangular matrix with the Fredholm-Rueppel sequence A036987 in every column: (1, 1, 0, 1, 0, 0, 0, 1,...); and B = an infinite lower triangular matrix with A023359: (1, 1, 2, 3, 6, 10, 18,...) as the main diagonal and the rest zeros.

%e First few rows of the triangle =

%e 1;

%e 1, 1;

%e 0, 1, 2;

%e 1, 0, 2, 3;

%e 0, 1, 0, 3, 6;

%e 0, 0, 2, 0, 6, 10;

%e 0, 0, 0, 3, 0, 10, 18;

%e 1, 0, 0, 0, 6, 0, 18, 31;

%e 0, 1, 0, 0, 0, 10, 0, 31, 56;

%e 0, 0, 2, 0, 0, 0, 18, 0, 56; 98;

%e 0, 0, 0, 3, 0, 0, 0, 31, 0, 98, 174;

%e 0, 0, 0, 0, 6, 0, 0, 0, 56, 0, 174, 306;

%e ...

%e Row 4 = (1, 0, 2, 3) = termwise products of (1, 0, 1, 1) and (1, 1, 2, 3).

%K nonn,tabl

%O 1,6

%A _Gary W. Adamson_, Sep 14 2008