%I
%S 1,0,3,0,0,5,0,0,2,9,0,0,0,3,12,0,0,0,2,9,20,0,0,0,0,3,11,25,0,0,0,0,
%T 2,9,22,38,0,0,0,0,0,3,14,28,49,0,0,0,0,0,2,9,26,44,69,0,0,0,0,0,0,3,
%U 14,37,55,87,0,0,0,0,0,0,2,9,29,62,83,123
%N Triangle read by rows: T(n,k) = sum of all parts in the kth column of the shell model of partitions considering only the nth shell and with its parts aligned to the right margin.
%e For n = 6 and k = 1..6 the 6th shell looks like this:
%e 
%e k: 1, 2, 3, 4, 5, 6
%e 
%e . 6
%e . 3 + 3
%e . 4 + 2
%e . 2 + 2 + 2
%e . 1
%e . 1
%e . 1
%e . 1
%e . 1
%e . 1
%e . 1
%e .
%e The sums of all parts in columns 16 are
%e . 0, 0, 0, 2, 9, 20, the same as the 6th row of triangle.
%e Triangle begins:
%e 1;
%e 0, 3;
%e 0, 0, 5;
%e 0, 0, 2, 9;
%e 0, 0, 0, 3, 12;
%e 0, 0, 0, 2, 9, 20;
%e 0, 0, 0, 0, 3, 11, 25;
%e 0, 0, 0, 0, 2, 9, 22, 38;
%e 0, 0, 0, 0, 0, 3, 14, 28, 49;
%e 0, 0, 0, 0, 0, 2, 9, 26, 44, 69;
%e 0, 0, 0, 0, 0, 0, 3, 14, 37, 55, 87;
%e 0, 0, 0, 0, 0, 0, 2, 9, 29, 62, 83, 123;
%Y Row sums give A138879. Column sums converge to A014153. Right border gives A046746, n >= 1.
%Y Cf. A135010, A138121, A210950, A210951, A210952.
%K nonn,tabl
%O 1,3
%A _Omar E. Pol_, Apr 22 2012
