

A194439


Number of regions of n that contain only one part.


16



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

1,4


COMMENTS

It appears that this is 1 together with A000041.  Omar E. Pol, Nov 29 2011
For the definition of "region of n" 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(n2), 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, A194438, A194446, A194447, A206437.
Sequence in context: A008641 A242698 A242699 * A046054 A242700 A242701
Adjacent sequences: A194436 A194437 A194438 * A194440 A194441 A194442


KEYWORD

nonn,more


AUTHOR

Omar E. Pol, Nov 28 2011


STATUS

approved



