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A241380 Number of partitions of n such that neither the number of parts nor the number of distinct parts is a part. 5
1, 0, 1, 1, 2, 2, 6, 6, 11, 13, 20, 26, 36, 48, 62, 84, 110, 142, 185, 235, 303, 384, 486, 612, 779, 949, 1205, 1481, 1846, 2248, 2812, 3390, 4181, 5070, 6195, 7450, 9102, 10896, 13199, 15785, 18994, 22660, 27177, 32262, 38482, 45722, 54224, 64125, 75934 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

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

FORMULA

a(n) + A241381(n) = A000041(n) for n >= 0.

EXAMPLE

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

MATHEMATICA

z = 30; f[n_] := f[n] = IntegerPartitions[n]; d[p_] := [p] = Length[DeleteDuplicates[p]];

Table[Count[f[n], p_ /; MemberQ[p, Length[p]] && MemberQ[p, d[p]]], {n, 0, z}]  (* A241377 *)

Table[Count[f[n], p_ /; ! MemberQ[p, Length[p]] && MemberQ[p, d[p]]], {n, 0, z}]  (* A241378 *)

Table[Count[f[n], p_ /; MemberQ[p, Length[p]] && ! MemberQ[p, d[p]]], {n, 0, z}]  (* A241379 *)

Table[Count[f[n], p_ /; ! MemberQ[p, Length[p]] && ! MemberQ[p, d[p]]], {n, 0, z}]  (* A241380 *)

Table[Count[f[n], p_ /; MemberQ[p, Length[p]] || MemberQ[p, d[p]]], {n, 0, z}] (* A241381 *)

CROSSREFS

Cf. A241377, A241378, A241379, A241381, A000041.

Sequence in context: A032139 A032043 A200561 * A028476 A179478 A051548

Adjacent sequences:  A241377 A241378 A241379 * A241381 A241382 A241383

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 21 2014

STATUS

approved

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Last modified April 6 21:24 EDT 2020. Contains 333286 sequences. (Running on oeis4.)