A194439 Number of regions in the set of partitions of n that contain only one part.

1, 1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176, 231, 297

Offset

1,4

Comments

It appears that this is 1 together with A000041. - Omar E. Pol, Nov 29 2011

For the definition of "region" see A206437. See also A186114 and A193870.

Links

Table of n, a(n) for n=1..19.

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

Formula

It appears that a(n) = A000041(n-2), if n >= 2. - Omar E. Pol, Nov 29 2011

It appears that a(n) = A000041(n) - A027336(n), if n >= 2. - Omar E. Pol, Nov 30 2011

Example

For n = 5 the seven regions of 5 in nondecreasing order are the sets of positive integers of the rows as shown below:
   1;
   1, 2;
   1, 1, 3;
   0, 0, 0, 2;
   1, 1, 1, 2, 4;
   0, 0, 0, 0, 0, 3;
   1, 1, 1, 1, 1, 2, 5;
   ...
There are three regions that contain only one positive part, so a(5) = 3.
Note that in every column of the triangle the positive integers are also the parts of one of the partitions of 5.

Crossrefs

Column 1 of A194438.

Cf. A000041, A002865, A027336, A135010, A138121, A186114, A186412, A193870, A194436, A194437, A194446, A194447, A206437.

Sequence in context: A364793 A330641 A242699 * A046054 A242700 A242701

Adjacent sequences: A194436 A194437 A194438 * A194440 A194441 A194442

Keyword

nonn,more

Author

Omar E. Pol, Nov 28 2011

Extensions

Definition clarified by Omar E. Pol, May 21 2021

Status

approved