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A000012 * A002865 as a diagonalized matrix.
1

%I #5 Mar 23 2022 01:05:29

%S 1,1,0,1,0,1,1,0,1,1,1,0,1,1,2,1,0,1,1,2,2,1,0,1,1,2,2,4,1,0,1,1,2,2,

%T 4,4,1,0,1,1,2,2,4,4,7,1,0,1,1,2,2,4,4,7,8

%N A000012 * A002865 as a diagonalized matrix.

%C Row sums = the partition numbers, A000041: (1, 1, 2, 3, 5, 7, 11, 15, ...).

%F A000012 * A002865 as a diagonalized matrix, the latter = an infinite lower triangular matrix with A002865: (1, 0, 1, 1, 2, 2, 4, 4, 7, 8, ...) as the main diagonal and the rest zeros. Triangle read by rows, n-th row = first (n+1) terms of A002865.

%e First few rows of the triangle:

%e 1;

%e 1, 0;

%e 1, 0, 1;

%e 1, 0, 1, 1;

%e 1, 0, 1, 1, 2;

%e 1, 0, 1, 1, 2, 2;

%e 1, 0, 1, 1, 2, 2, 4;

%e 1, 0, 1, 1, 2, 2, 4, 4;

%e 1, 0, 1, 1, 2, 2, 4, 4, 7;

%e ...

%Y Cf. A000041, A002865.

%K nonn,tabl

%O 0,15

%A _Gary W. Adamson_, Sep 22 2007