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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
0, 1, 1, 2, 2, 4, 5, 7, 10, 15, 20, 25, 40, 45, 68, 84, 115, 141, 195, 235, 317, 386, 504, 617, 788, 970, 1224, 1493, 1862, 2275, 2802, 3401, 4191, 5044, 6144, 7423, 8962, 10758, 12966, 15469, 18586, 22114, 26376, 31300, 37285, 43986, 52182, 61501, 72647 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

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

FORMULA

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

EXAMPLE

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

MATHEMATICA

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

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

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

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

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

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

CROSSREFS

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

Sequence in context: A238594 A239945 A238875 * A241736 A034398 A277062

Adjacent sequences:  A241388 A241389 A241390 * A241392 A241393 A241394

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 21 2014

STATUS

approved

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Last modified October 22 02:52 EDT 2020. Contains 337950 sequences. (Running on oeis4.)