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

1,2

Comments

For another version see A207379.

Links

Alois P. Heinz, Rows n = 1..70

Example

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;

Crossrefs

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

Cf. A135010, A138121, A182717, A207379.

Sequence in context: A322558 A139047 A343376 * A191795 A330612 A121053

Adjacent sequences: A210942 A210943 A210944 * A210946 A210947 A210948

Keyword

nonn,tabf

Author

Omar E. Pol, Apr 21 2012

Extensions

More terms from Alois P. Heinz, May 07 2012

Status

approved