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A237752 Number of partitions of n such that 2*(greatest part) <= (number of parts). 3
0, 1, 1, 1, 2, 3, 4, 6, 7, 10, 13, 18, 23, 31, 39, 50, 64, 82, 102, 130, 162, 203, 252, 313, 384, 475, 580, 710, 864, 1053, 1273, 1544, 1859, 2240, 2688, 3224, 3851, 4602, 5476, 6514, 7727, 9160, 10826, 12791, 15072, 17747, 20853, 24481, 28679, 33577, 39231 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

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 a part of p.

LINKS

Table of n, a(n) for n=1..51.

FORMULA

a(n) + A237754(n) = A000041(n).

EXAMPLE

The partitions of 6 that do not qualify are 22311, 21111, 111111, so that a(6) = 11 - 3 = 8.

MATHEMATICA

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

(* also *)

Table[Count[IntegerPartitions[n], p_ /; MemberQ[p, Max[Max[p], 2*Length[p]]]], {n, 50}]

CROSSREFS

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

Sequence in context: A199118 A035941 A039854 * A032480 A226137 A163771

Adjacent sequences:  A237749 A237750 A237751 * A237753 A237754 A237755

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 13 2014

STATUS

approved

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Last modified September 19 17:40 EDT 2020. Contains 337179 sequences. (Running on oeis4.)