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A237754 Number of partitions of n such that 2*(greatest part) > (number of parts). 2
1, 1, 2, 4, 5, 8, 11, 16, 23, 32, 43, 59, 78, 104, 137, 181, 233, 303, 388, 497, 630, 799, 1003, 1262, 1574, 1961, 2430, 3008, 3701, 4551, 5569, 6805, 8284, 10070, 12195, 14753, 17786, 21413, 25709, 30824, 36856, 44014, 52435, 62384, 74062, 87811, 103901 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Also, the number of partitions of n such that (greatest part) < 2*(number of parts); hence, the number of partitions of n such that (rank + greatest part) > 0.

Also, the number of partitions p of n such that max(max(p), 2*(number of parts of p)) is not a part of p.

LINKS

Table of n, a(n) for n=1..47.

FORMULA

a(n) + A237752(n) = A000041(n).

EXAMPLE

a(5) = 5 counts these partitions:  5, 41, 32, 311, 221.

MATHEMATICA

z = 50; Table[Count[IntegerPartitions[n], p_ /; 2 Max[p] > Length[p]], {n, z}]

CROSSREFS

Cf. A064173, A237751-A237753, A237755-A237757, A000041.

Sequence in context: A205728 A074824 A039867 * A182564 A288523 A240179

Adjacent sequences:  A237751 A237752 A237753 * A237755 A237756 A237757

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 13 2014

STATUS

approved

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Last modified September 27 03:21 EDT 2020. Contains 337380 sequences. (Running on oeis4.)