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.

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, 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, 14, 37, 55, 87, 0, 0, 0, 0, 0, 0, 2, 9, 29, 62, 83, 123

Offset: 1

Author

Omar E. Pol, Apr 22 2012

Keywords

• nonn
• tabl

Examples

			For n = 6 and k = 1..6 the 6th shell looks like this:
-------------------------
k: 1,  2,  3,  4,  5,  6
-------------------------
.                      6
.                  3 + 3
.                  4 + 2
.              2 + 2 + 2
.                      1
.                      1
.                      1
.                      1
.                      1
.                      1
.                      1
.
The sums of all parts in columns 1-6 are
.  0,  0,  0,  2,  9, 20, the same as the 6th row of triangle.
Triangle begins:
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,  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, 14, 37, 55, 87;
0, 0, 0, 0,  0,  0,  2,  9, 29, 62, 83, 123;
		

Crossrefs

Row sums give A138879. Column sums converge to A014153. Right border gives A046746, n >= 1.

Cf. A135010, A138121, A210950, A210951, A210952.