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A210952
Triangle read by rows: T(n,k) = sum of all parts of the k-th column of the partitions of n but with the partitions aligned to the right margin.
8
1, 1, 3, 1, 3, 5, 1, 3, 7, 9, 1, 3, 7, 12, 12, 1, 3, 7, 14, 21, 20, 1, 3, 7, 14, 24, 31, 25, 1, 3, 7, 14, 26, 40, 47, 38, 1, 3, 7, 14, 26, 43, 61, 66, 49, 1, 3, 7, 14, 26, 45, 70, 92, 93, 69, 1, 3, 7, 14, 26, 45, 73, 106, 130, 124, 87, 1, 3, 7, 14
OFFSET
1,3
FORMULA
T(n,k) = Sum_{j=1..n} A210953(j,k). - Omar E. Pol, May 26 2012
EXAMPLE
For n = 6 the illustration shows the partitions of 6 aligned to the right margin and below the sums of the columns:
.
. 6
. 3 + 3
. 4 + 2
. 2 + 2 + 2
. 5 + 1
. 3 + 2 + 1
. 4 + 1 + 1
. 2 + 2 + 1 + 1
. 3 + 1 + 1 + 1
. 2 + 1 + 1 + 1 + 1
. 1 + 1 + 1 + 1 + 1 + 1
-------------------------
. 1, 3, 7, 14, 21, 20
.
So row 6 lists 1, 3, 7, 14, 21, 20.
Triangle begins:
1;
1, 3;
1, 3, 5;
1, 3, 7, 9;
1, 3, 7, 12, 12;
1, 3, 7, 14, 21, 20;
1, 3, 7, 14, 24, 31, 25;
1, 3, 7, 14, 26, 40, 47, 38;
1, 3, 7, 14, 26, 43, 61, 66, 49;
1, 3, 7, 14, 26, 45, 70, 92, 93, 69:
CROSSREFS
Mirror of triangle A206283. Rows sums give A066186. Rows converge to A014153. Right border gives A046746, >= 1.
Sequence in context: A113759 A294966 A258208 * A208523 A209572 A134231
KEYWORD
nonn,tabl
AUTHOR
Omar E. Pol, Apr 22 2012
STATUS
approved