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A210950 Triangle read by rows: T(n,k) = number of parts in the k-th column of the partitions of n but with the partitions aligned to the right margin. 3
1, 1, 2, 1, 2, 3, 1, 2, 4, 5, 1, 2, 4, 6, 7, 1, 2, 4, 7, 10, 11, 1, 2, 4, 7, 11, 14, 15, 1, 2, 4, 7, 12, 17, 21, 22, 1, 2, 4, 7, 12, 18, 25, 29, 30, 1, 2, 4, 7, 12, 19, 28, 36, 41, 42, 1, 2, 4, 7, 12, 19, 29, 40, 50, 55, 56, 1, 2, 4, 7, 12, 19, 30, 43 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..74.

FORMULA

T(n,k) = Sum_{j=1..n} A210951(j,k).

EXAMPLE

For n = 6 the partitions of 6 aligned to the right margin look like this:

.

.                      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

.

The number of parts in columns 1-6 are

.  1,  2,  4,  7, 10, 11, the same as the 6th row of triangle.

Triangle begins:

1;

1, 2;

1, 2, 3;

1, 2, 4, 5;

1, 2, 4, 6, 7;

1, 2, 4, 7, 10, 11;

1, 2, 4, 7, 11, 14, 15;

1, 2, 4, 7, 12, 17, 21, 22;

1, 2, 4, 7, 12, 18, 25, 29, 30;

1, 2, 4, 7, 12, 19, 28, 36, 41, 42;

1, 2, 4, 7, 12, 19, 29, 40, 50, 55, 56;

1, 2, 4, 7, 12, 19, 30, 43, 58, 70, 76, 77;

CROSSREFS

Mirror of A058399. Row sums give A006128. Right border gives A000041, n >= 1. Rows converge to A000070.

Cf. A135010, A194714, A210945, A210951, A210952, A210953, A210970.

Sequence in context: A145111 A104795 A116925 * A214314 A209435 A263744

Adjacent sequences:  A210947 A210948 A210949 * A210951 A210952 A210953

KEYWORD

nonn,tabl

AUTHOR

Omar E. Pol, Apr 22 2012

STATUS

approved

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Last modified November 24 00:27 EST 2017. Contains 295164 sequences.