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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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..70.

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.

Cf. A135010, A138121, A181187, A210763, A210950, A210951, A210953, A210961, A210970.

Sequence in context: A113759 A294966 A258208 * A208523 A209572 A134231

Adjacent sequences:  A210949 A210950 A210951 * A210953 A210954 A210955

KEYWORD

nonn,tabl

AUTHOR

Omar E. Pol, Apr 22 2012

STATUS

approved

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Last modified April 6 12:08 EDT 2020. Contains 333273 sequences. (Running on oeis4.)