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Triangle read by rows, modified version of A161363; row sums = A000041
4

%I #3 Mar 30 2012 17:25:34

%S 1,1,0,2,0,0,2,1,0,0,4,1,0,0,0,3,2,2,0,0,0,7,2,2,0,0,0,0,7,3,2,3,0,0,

%T 0,0,12,3,4,3,0,0,0,0,0,13,5,4,3,5,0,0,0,0,0,22,6,6,3,5,0,0,0,0,0,0,2,

%U 5,7,6,6,5,7,0,0,0,0,0,0,4,9,8,6,5,7,0,0,0,0,0,0,0

%N Triangle read by rows, modified version of A161363; row sums = A000041

%C Row sums = A000041, the partition numbers.

%F Given triangle A161363, (the inverse of partition triangle A026794); multiply by (-1), delete right border of 1's, and shift down 1 row inserting a "1" at T(0,0); = triangle M. Let Q = an infinite lower triangular matrix with A000041 as the right border and the rest zeros. Triangle A161364 = M * Q.

%e First few rows of the triangle =

%e 1;

%e 1, 0;

%e 2, 0, 0;

%e 2, 1, 0, 0;

%e 4, 1, 0, 0, 0;

%e 3, 2, 2, 0, 0, 0;

%e 7, 2, 2, 0, 0, 0, 0;

%e 7, 3, 2, 3, 0, 0, 0, 0;

%e 12, 3, 4, 3, 0, 0, 0, 0, 0;

%e 13, 5, 4, 3, 5, 0, 0, 0, 0, 0;

%e 22, 6, 6, 3, 5, 0, 0, 0, 0, 0, 0;

%e 25, 7, 6, 6, 5, 7, 0, 0, 0, 0, 0, 0;

%e 42, 9, 8, 6, 5, 7, 0, 0, 0, 0, 0, 0, 0;

%e 48, 13, 8, 9, 5, 7, 11, 0, 0, 0, 0, 0, 0, 0;

%e ...

%Y A161363, A000041

%K nonn,tabl

%O 0,4

%A _Gary W. Adamson_, Jun 07 2009