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A210951 Triangle read by rows: T(n,k) = number of 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 A210951 #20 Mar 12 2015 23:22:52
%S A210951 1,0,2,0,0,3,0,0,1,5,0,0,0,1,7,0,0,0,1,3,11,0,0,0,0,1,3,15,0,0,0,0,1,
%T A210951 3,6,22,0,0,0,0,0,1,4,7,30,0,0,0,0,0,1,3,7,11,42,0,0,0,0,0,0,1,4,9,13,
%U A210951 56,0,0,0,0,0,0,1,3,8,15,20,77,0,0,0
%N A210951 Triangle read by rows: T(n,k) = number of 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 A210951 For n = 6 and k = 1..6 the 6th shell looks like this:
%e A210951 -------------------------
%e A210951 k: 1,  2,  3,  4,  5,  6
%e A210951 -------------------------
%e A210951 .                      6
%e A210951 .                  3 + 3
%e A210951 .                  4 + 2
%e A210951 .              2 + 2 + 2
%e A210951 .                      1
%e A210951 .                      1
%e A210951 .                      1
%e A210951 .                      1
%e A210951 .                      1
%e A210951 .                      1
%e A210951 .                      1
%e A210951 .
%e A210951 The total number of parts in columns 1-6 are
%e A210951 .  0,  0,  0,  1,  3, 11, the same as the 6th row of triangle.
%e A210951 Triangle begins:
%e A210951 1;
%e A210951 0, 2;
%e A210951 0, 0, 3;
%e A210951 0, 0, 1, 5;
%e A210951 0, 0, 0, 1, 7;
%e A210951 0, 0, 0, 1, 3, 11;
%e A210951 0, 0, 0, 0, 1, 3, 15;
%e A210951 0, 0, 0, 0, 1, 3, 6, 22;
%e A210951 0, 0, 0, 0, 0, 1, 4, 7, 30;
%e A210951 0, 0, 0, 0, 0, 1, 3, 7, 11, 42;
%e A210951 0, 0, 0, 0, 0, 0, 1, 4, 9, 13, 56;
%e A210951 0, 0, 0, 0, 0, 0, 1, 3, 8, 15, 20, 77;
%Y A210951 Row sums give A138137. Column sums converge to A000070. Right border gives A000041, n >= 1.
%Y A210951 Cf. A135010, A138121, A194714, A210945, A210950, A210952, A210953.
%K A210951 nonn,tabl
%O A210951 1,3
%A A210951 _Omar E. Pol_, Apr 22 2012