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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.
5
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.
Sequence in context: A322558 A139047 A343376 * A372112 A191795 A330612
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Apr 21 2012
EXTENSIONS
More terms from Alois P. Heinz, May 07 2012
STATUS
approved