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A210953 Triangle read by rows: T(n,k) = sum of all parts in the k-th column of the shell model of partitions considering only the n-th shell and with its parts aligned to the right margin.

%I A210953 #15 Mar 12 2015 23:23:05
%S A210953 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 A210953 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 A210953 14,37,55,87,0,0,0,0,0,0,2,9,29,62,83,123
%N A210953 Triangle read by rows: T(n,k) = sum of all parts in the k-th column of the shell model of partitions considering only the n-th shell and with its parts aligned to the right margin.
%e A210953 For n = 6 and k = 1..6 the 6th shell looks like this:
%e A210953 -------------------------
%e A210953 k: 1,  2,  3,  4,  5,  6
%e A210953 -------------------------
%e A210953 .                      6
%e A210953 .                  3 + 3
%e A210953 .                  4 + 2
%e A210953 .              2 + 2 + 2
%e A210953 .                      1
%e A210953 .                      1
%e A210953 .                      1
%e A210953 .                      1
%e A210953 .                      1
%e A210953 .                      1
%e A210953 .                      1
%e A210953 .
%e A210953 The sums of all parts in columns 1-6 are
%e A210953 .  0,  0,  0,  2,  9, 20, the same as the 6th row of triangle.
%e A210953 Triangle begins:
%e A210953 1;
%e A210953 0, 3;
%e A210953 0, 0, 5;
%e A210953 0, 0, 2, 9;
%e A210953 0, 0, 0, 3, 12;
%e A210953 0, 0, 0, 2,  9, 20;
%e A210953 0, 0, 0, 0,  3, 11, 25;
%e A210953 0, 0, 0, 0,  2,  9, 22, 38;
%e A210953 0, 0, 0, 0,  0,  3, 14, 28, 49;
%e A210953 0, 0, 0, 0,  0,  2,  9, 26, 44, 69;
%e A210953 0, 0, 0, 0,  0,  0,  3, 14, 37, 55, 87;
%e A210953 0, 0, 0, 0,  0,  0,  2,  9, 29, 62, 83, 123;
%Y A210953 Row sums give A138879. Column sums converge to A014153. Right border gives A046746, n >= 1.
%Y A210953 Cf. A135010, A138121, A210950, A210951, A210952.
%K A210953 nonn,tabl
%O A210953 1,3
%A A210953 _Omar E. Pol_, Apr 22 2012