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A279036 Number of partitions p of n that contain a proper partition of the maximal part of p. 0
0, 0, 0, 1, 1, 4, 4, 10, 12, 21, 25, 46, 50, 82, 99, 148, 175, 259, 303, 435, 513, 708, 845, 1146, 1347, 1802, 2138, 2793, 3318, 4273, 5050, 6471, 7621, 9641, 11406, 14210, 16758, 20833, 24475, 30143 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

Table of n, a(n) for n=1..40.

EXAMPLE

a(8) counts these 10 partitions:  [4,3,1], [4,2,2], [4,2,1,1], [4,1,1,1,1], [3,2,2,1], [3,2,1,1,1], [3,1,1,1,1,1], [2,2,2,1,1], [2,2,1,1,1,1],[2,1,1,1,1,1,1]; e.g., [3,1] is a proper partition of 4.

MATHEMATICA

Table[parts = IntegerPartitions[z]; parts = Drop[parts,

Position[Map[#[[1]] &, parts], Floor[z/2], 1, 1][[1]][[1]] - 1];

Count[Table[{first, rest} = {First[#], Rest[#]} &[parts[[nn]]];

Apply[Or, Map[MatchQ[rest, #] &, Map[Flatten[{___, #, ___}] &,

Rest[IntegerPartitions[first]]]]], {nn, Length[parts]}], True], {z, 30}]

(* Peter J. C. Moses, Dec 02 2016 *)

CROSSREFS

Cf. A000041.

Sequence in context: A219471 A006477 A233739 * A182699 A058596 A180964

Adjacent sequences:  A279033 A279034 A279035 * A279037 A279038 A279039

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Dec 04 2016

STATUS

approved

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Last modified September 21 02:46 EDT 2020. Contains 337266 sequences. (Running on oeis4.)