A210969 Sum of all region numbers of all parts of the last section of the set of partitions of n.

1, 4, 9, 29, 55, 157, 277, 669, 1212, 2555, 4459, 9048

Offset: 1

Author

Omar E. Pol, Jul 01 2012

Keywords

• nonn
• more

Comments

Each part of a partition of n belongs to a different region of n. The "region number" of a part of the r-th region of n is equal to r. For the definition of "region of n" see A206437.

The last section of the set of partitions of n is also the n-th section of the set of partitions of any integer >= n. - Omar E. Pol, Apr 07 2014

Examples

			For n = 6 the four regions of the last section of 6 are [2], [4, 2], [3], [6, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1] therefore the "region numbers" are [8], [9, 9], [10], [11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11]. The sum of all region numbers is a(6) = 8+2*9+10+11^2 =  8+18+10+121 = 157, see below:
--------------------------------------------
.     Last section                  Sum of
.     of the set of     Region      region
k    partitions of 6    numbers     numbers
--------------------------------------------
11           6              11         11
10         3+3           10,11         21
9        4  +2         9,   11         20
8      2+2  +2       8,9,   11         28
7            1              11         11
6            1              11         11
5            1              11         11
4            1              11         11
3            1              11         11
2            1              11         11
1            1              11         11
--------------------------------------------
Total sum of region numbers is a(6) = 157
		

Links

• Omar E. Pol, Illustration of the seven regions of 5

Crossrefs

Row sums of triangle A210966. Partial sums give A210972.

Cf. A135010, A138121, A194446, A182703, A206437, A210971.