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A210945
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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.
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5
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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
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OFFSET
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1,2
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COMMENTS
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LINKS
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EXAMPLE
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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;
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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