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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

%I

%S 1,0,1,1,2,2,6,6,11,13,20,26,36,48,62,84,110,142,185,235,303,384,486,

%T 612,779,949,1205,1481,1846,2248,2812,3390,4181,5070,6195,7450,9102,

%U 10896,13199,15785,18994,22660,27177,32262,38482,45722,54224,64125,75934

%N Number of partitions of n such that neither the number of parts nor the number of distinct parts is a part.

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

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

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

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

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

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

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

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

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

%K nonn,easy

%O 0,5

%A _Clark Kimberling_, Apr 21 2014

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Last modified May 27 12:45 EDT 2020. Contains 334657 sequences. (Running on oeis4.)