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A241385 Number of partitions p of n such that the number of parts is not a part and max(p) - min(p) is not a part. 5
1, 0, 2, 2, 3, 3, 7, 7, 12, 15, 23, 32, 42, 56, 78, 100, 133, 174, 224, 292, 375, 479, 614, 783, 978, 1236, 1545, 1925, 2386, 2963, 3640, 4494, 5497, 6731, 8201, 9994, 12098, 14673, 17698, 21339, 25632, 30788, 36816, 44035, 52480, 62504, 74253, 88133, 104307 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..48.

FORMULA

a(n) + A241386(n) = A000041(n) for n >= 0.

EXAMPLE

a(6) counts these 7 partitions:  6, 51, 411, 33, 3111, 222, 111111.

MATHEMATICA

z = 40; f[n_] := f[n] = IntegerPartitions[n];

Table[Count[f[n], p_ /; MemberQ[p, Length[p]] && MemberQ[p, Max[p] - Min[p]]], {n, 0, z}]  (* A241382 *)

Table[Count[f[n],  p_ /; ! MemberQ[p, Length[p]] && MemberQ[p, Max[p] - Min[p]]], {n, 0, z}]  (* A241383 *)

Table[Count[f[n], p_ /; MemberQ[p, Length[p]] && ! MemberQ[p, Max[p] - Min[p]]], {n, 0, z}]  (* A241384 *)

Table[Count[f[n], p_ /; ! MemberQ[p, Length[p]] && ! MemberQ[p, Max[p] - Min[p]]], {n, 0, z}]  (* A241385 *)

Table[Count[f[n], p_ /; MemberQ[p, Length[p]] || MemberQ[p, Max[p] - Min[p]]], {n, 0, z}]  (* A241386 *)

CROSSREFS

Cf. A241382, A241383, A241384, A241386.

Sequence in context: A309684 A330950 A032060 * A307736 A309713 A153903

Adjacent sequences:  A241382 A241383 A241384 * A241386 A241387 A241388

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 21 2014

STATUS

approved

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Last modified October 26 11:29 EDT 2020. Contains 338027 sequences. (Running on oeis4.)