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A241391 Number of partitions p of n such that the number of distinct parts is a part or max(p) - min(p) is a part. 5

%I #4 Apr 27 2014 10:25:50

%S 0,1,1,2,2,4,5,7,10,15,20,25,40,45,68,84,115,141,195,235,317,386,504,

%T 617,788,970,1224,1493,1862,2275,2802,3401,4191,5044,6144,7423,8962,

%U 10758,12966,15469,18586,22114,26376,31300,37285,43986,52182,61501,72647

%N Number of partitions p of n such that the number of distinct parts is a part or max(p) - min(p) is a part.

%F a(n) + A241390(n) = A000041(n) for n >= 0.

%e a(6) counts these 5 partitions: 42, 321, 2211, 21111, 111111.

%t z = 40; f[n_] := f[n] = IntegerPartitions[n]; d[p_] := d[p] = Length[DeleteDuplicates[p]];

%t Table[Count[f[n], p_ /; MemberQ[p, d[p]] && MemberQ[p, Max[p] - Min[p]]], {n, 0, z}] (* A241387 *)

%t Table[Count[f[n], p_ /; ! MemberQ[p, d[p]] && MemberQ[p, Max[p] - Min[p]]], {n, 0, z}] (* A241388 *)

%t Table[Count[f[n], p_ /; MemberQ[p, d[p]] && ! MemberQ[p, Max[p] - Min[p]]], {n, 0, z}] (* A241389 *)

%t Table[Count[f[n], p_ /; ! MemberQ[p, d[p]] && ! MemberQ[p, Max[p] - Min[p]]], {n, 0, z}] (* A241390 *)

%t Table[Count[f[n], p_ /; MemberQ[p, d[p]] || MemberQ[p, Max[p] - Min[p]]], {n, 0, z}] (* A241391 *)

%Y Cf. A241387, A241388, A241389, A241390, A000041.

%K nonn,easy

%O 0,4

%A _Clark Kimberling_, Apr 21 2014

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)