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

1,3

Links

Table of n, a(n) for n=1..78.

Example

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.

Sequence in context: A361357 A305151 A127775 * A254280 A092669 A255986

Adjacent sequences: A210950 A210951 A210952 * A210954 A210955 A210956

Keyword

nonn,tabl

Author

Omar E. Pol, Apr 22 2012

Status

approved