A211004 Number of distinct regions in the set of partitions of n.

1, 2, 3, 5, 7, 9, 12, 15, 18, 22, 26, 30, 35, 40, 45, 51

Offset

1,2

Comments

The number of regions in the set of partitions of n equals the number of partitions of n. The sequence counts only the distinct regions. For the definition of "regions of the set of partitions of n" (or more simply "regions of n") see A206437.

Is this the same as A001840 for all positive integers? If not, where is the first place these sequences differ?

Links

Table of n, a(n) for n=1..16.

Omar E. Pol, Illustration of initial terms

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

Example

For n = 6 the 11 regions of 6 are [1], [2,1], [3,1,1], [2], [4,2,1,1,1], [3], [5,2,1,1,1,1,1], [2], [4,2], [3], [6,3,2,2,1,1,1,1,1,1,1]. These number are the first A006128(6) terms of triangle A206437 in which the first A000041(6) rows are the 11 regions of 6. We can see that the 8th region is equal to the 4th region: [2] = [2]. Also the 10th region is equal to the 6th region: [3] = [3]. There are two repeated regions, therefore a(6) = A000041(6) - 2 = 11 - 2 = 9.

Crossrefs

Cf. A000041, A006128, A135010, A141285, A182244, A186114, A186412, A187219, A193870, A194446, A194447, A206437, A211009.

Sequence in context: A184017 A024195 A071423 * A062781 A145919 A058937

Adjacent sequences: A211001 A211002 A211003 * A211005 A211006 A211007

Keyword

nonn,more

Author

Omar E. Pol, Oct 22 2012

Status

approved