

A210950


Triangle read by rows: T(n,k) = number of parts in the kth 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
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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 16 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



