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A210951
Triangle read by rows: T(n,k) = number of 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.
3
1, 0, 2, 0, 0, 3, 0, 0, 1, 5, 0, 0, 0, 1, 7, 0, 0, 0, 1, 3, 11, 0, 0, 0, 0, 1, 3, 15, 0, 0, 0, 0, 1, 3, 6, 22, 0, 0, 0, 0, 0, 1, 4, 7, 30, 0, 0, 0, 0, 0, 1, 3, 7, 11, 42, 0, 0, 0, 0, 0, 0, 1, 4, 9, 13, 56, 0, 0, 0, 0, 0, 0, 1, 3, 8, 15, 20, 77, 0, 0, 0
OFFSET
1,3
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 total number of parts in columns 1-6 are
. 0, 0, 0, 1, 3, 11, the same as the 6th row of triangle.
Triangle begins:
1;
0, 2;
0, 0, 3;
0, 0, 1, 5;
0, 0, 0, 1, 7;
0, 0, 0, 1, 3, 11;
0, 0, 0, 0, 1, 3, 15;
0, 0, 0, 0, 1, 3, 6, 22;
0, 0, 0, 0, 0, 1, 4, 7, 30;
0, 0, 0, 0, 0, 1, 3, 7, 11, 42;
0, 0, 0, 0, 0, 0, 1, 4, 9, 13, 56;
0, 0, 0, 0, 0, 0, 1, 3, 8, 15, 20, 77;
CROSSREFS
Row sums give A138137. Column sums converge to A000070. Right border gives A000041, n >= 1.
Sequence in context: A259480 A280164 A049597 * A348127 A233440 A280728
KEYWORD
nonn,tabl
AUTHOR
Omar E. Pol, Apr 22 2012
STATUS
approved