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

1,2

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

Links

Table of n, a(n) for n=1..12.

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

Example

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

Crossrefs

Row sums of triangle A210966. Partial sums give A210972.

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

Sequence in context: A069563 A352878 A276984 * A059345 A127768 A231255

Adjacent sequences: A210966 A210967 A210968 * A210970 A210971 A210972

Keyword

nonn,more

Author

Omar E. Pol, Jul 01 2012

Status

approved