A210972 Sum of all region numbers of all parts of all partitions of n.

1, 5, 14, 43, 98, 255, 532, 1201, 2413, 4968, 9427, 18475

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.

Links

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

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

Example

For n = 5 we have:
---------------------------------------------------
.              Two arrangements
k           of the partitions of 5
---------------------------------------------------
7      [5]                          [5]
6      [3+2]                      [3+2]
5      [4+1]                    [4  +1]
4      [2+1+1]                [2+2  +1]
3      [3+1+1]              [3  +1  +1]
2      [2+1+1+1]          [2+1  +1  +1]
1      [1+1+1+1+1]      [1+1+1  +1  +1]
---------------------------------------------------
.              Two arrangements
.           of the region numbers           Sum of
k           of the partitions of 5          zone k
---------------------------------------------------
7      [7]                          [7]        7
6      [6,7]                      [6,7]       13
5      [5,7]                    [5,  7]       12
4      [4,5,7]                [4,5,  7]       16
3      [3,5,7]              [3,  5,  7]       15
2      [2,3,5,7]          [2,3,  5,  7]       17
1      [1,2,3,5,7]      [1,2,3,  5,  7]       18
---------------------------------------------------
The total sum is a(5) = 1+2^2+3^2+4+5^2+6+7^2 = 1+4+9+4+25+6+49 = 18+17+15+16+12+13+7 = 98.

Crossrefs

Partial sums of A210969. Row sums of triangle A210971.

Cf. A135010, A138121, A182703, A194446, A210437, A210966.

Sequence in context: A034549 A232492 A180774 * A197607 A296829 A102434

Adjacent sequences: A210969 A210970 A210971 * A210973 A210974 A210975

Keyword

nonn,more

Author

Omar E. Pol, Jun 30 2012

Status

approved