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A241416 Number of partitions p of n such that the number of numbers having multiplicity 1 in p is a part and the number of numbers having multiplicity > 1 is not a part. 7
0, 1, 0, 1, 0, 1, 2, 1, 2, 3, 4, 4, 8, 14, 16, 28, 33, 47, 61, 83, 98, 131, 157, 201, 248, 312, 379, 480, 589, 730, 903, 1136, 1373, 1725, 2095, 2593, 3129, 3870, 4625, 5677, 6774, 8215, 9759, 11813, 13896, 16738, 19675, 23515, 27580, 32846, 38349, 45528 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

LINKS

Table of n, a(n) for n=0..51.

FORMULA

a(n) + A241414(n) + A241415(n) = A239737(n) for n >= 0.

EXAMPLE

a(6) counts these 2 partitions:  42, 321.

MATHEMATICA

z = 30; f[n_] := f[n] = IntegerPartitions[n]; u[p_] := Length[DeleteDuplicates[Select[p, Count[p, #] ==  &]]]; e[q_] := Length[DeleteDuplicates[Select[q, Count[q, #] > 1 &]]]

Table[Count[f[n], p_ /; MemberQ[p, u[p]]], {n, 0, z}]  (* A241413 *)

Table[Count[f[n], p_ /; MemberQ[p, u[p]] && MemberQ[p, e[p]]], {n, 0, z}]  (* A241414 *)

Table[Count[f[n], p_ /; ! MemberQ[p, u[p]] && MemberQ[p, e[p]] ], {n, 0, z}] (* A241415 *)

Table[Count[f[n], p_ /; MemberQ[p, u[p]] && ! MemberQ[p, e[p]] ], {n, 0, z}] (* A241416 *)

Table[Count[f[n], p_ /; ! MemberQ[p, u[p]] && ! MemberQ[p, e[p]] ], {n, 0, z}] (* A241417 *)

Table[Count[f[n], p_ /; MemberQ[p, u[p]] || MemberQ[p, e[p]] ], {n, 0, z}] (* A239737 *)

CROSSREFS

Cf. A241413, A241414, A241415, A241417, A239737.

Sequence in context: A281544 A056882 A035534 * A082854 A086742 A133182

Adjacent sequences:  A241413 A241414 A241415 * A241417 A241418 A241419

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 23 2014

STATUS

approved

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Last modified October 20 22:44 EDT 2019. Contains 328291 sequences. (Running on oeis4.)