A210945 Triangle read by rows: T(n,k) = number of parts in the k-th column of the mirror of the last shell of the partitions of n.

1, 2, 3, 5, 1, 7, 1, 11, 3, 1, 15, 3, 1, 22, 6, 3, 1, 30, 7, 4, 1, 42, 11, 7, 3, 1, 56, 13, 9, 4, 1, 77, 20, 15, 8, 3, 1, 101, 23, 18, 10, 4, 1, 135, 33, 27, 17, 8, 3, 1, 176, 40, 34, 22, 11, 4, 1, 231, 54, 47, 33, 18, 8, 3, 1, 297, 65, 58, 42, 24, 11, 4, 1

Offset: 1

Author

Omar E. Pol, Apr 21 2012

Keywords

• nonn
• tabf

Comments

For another version see A207379.

Examples

			For n = 7 the illustration shows two arrangements of the last shell of the partitions of 7:
.
.       (7)        (7)
.     (4+3)        (3+4)
.     (5+2)        (2+5)
.   (3+2+2)        (2+2+3)
.       (1)        (1)
.       (1)        (1)
.       (1)        (1)
.       (1)        (1)
.       (1)        (1)
.       (1)        (1)
.       (1)        (1)
.       (1)        (1)
.       (1)        (1)
.       (1)        (1)
.       (1)        (1)
.                 --------
.                  15,3,1
.
We can see that in the right hand picture (the mirror) the number of part for columns 1..3 are 15, 3, 1 therefore row 7 lists 15, 3, 1.
Written as a triangle begins:
1;
2;
3;
5,    1;
7,    1;
11,   3,  1;
15,   3,  1;
22,   6,  3,  1;
30,   7,  4,  1;
42,  11,  7,  3,  1;
56,  13,  9,  4,  1;
77,  20, 15,  8,  3,  1;
101, 23, 18, 10,  4,  1;
135, 33, 27, 17,  8,  3,  1;
176, 40, 34, 22, 11,  4,  1;
231, 54, 47, 33, 18,  8,  3,  1;
297, 65, 58, 42, 24, 11,  4,  1;
		

Links

• Alois P. Heinz, Rows n = 1..70

Crossrefs

Column 1 is A000041,n >= 1. Column 2 is A083751. Column 3 is A119907. Row sums give A138137.

Cf. A135010, A138121, A182717, A207379.

Extensions

More terms from Alois P. Heinz, May 07 2012