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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 (list; graph; refs; listen; history; text; internal format)
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(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, 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

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Last modified June 18 18:52 EDT 2019. Contains 324215 sequences. (Running on oeis4.)