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A210972 Sum of all region numbers of all parts of all partitions of n. 3
1, 5, 14, 43, 98, 255, 532, 1201, 2413, 4968, 9427, 18475 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 19 01:11 EST 2021. Contains 340262 sequences. (Running on oeis4.)