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A241508 Number of partitions of n such that (number parts having multiplicity 1) is a part and (number of 1s) is not a part. 5
0, 0, 0, 0, 0, 3, 3, 5, 5, 10, 10, 17, 21, 34, 36, 60, 70, 97, 119, 165, 199, 275, 324, 424, 526, 685, 806, 1057, 1263, 1586, 1918, 2409, 2868, 3584, 4266, 5239, 6282, 7679, 9068, 11086, 13157, 15809, 18776, 22536, 26558, 31833, 37429, 44465, 52373, 62037 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,6
LINKS
FORMULA
a(n) + A241506(n) + A241507(n) = A241510(n) for n >= 0.
EXAMPLE
a(6) counts these 3 partitions: 42, 411, 2111.
MATHEMATICA
z = 52; f[n_] := f[n] = IntegerPartitions[n]; u[p_] := Length[DeleteDuplicates[Select[p, Count[p, #] == 1 &]]];
Table[Count[f[n], p_ /; MemberQ[p, u[p]] && MemberQ[p, Count[p, 1]]], {n, 0, z}] (* A241506 *)
Table[Count[f[n], p_ /; ! MemberQ[p, u[p]] && MemberQ[p, Count[p, 1]] ], {n, 0, z}] (* A241507 *)
Table[Count[f[n], p_ /; MemberQ[p, u[p]] && ! MemberQ[p, Count[p, 1]] ], {n, 0, z}] (* A241508 *)
Table[Count[f[n], p_ /; ! MemberQ[p, u[p]] && ! MemberQ[p, Count[p, 1]] ], {n, 0, z}] (* A241509 *)
Table[Count[f[n], p_ /; MemberQ[p, u[p]] || MemberQ[p, Count[p, 1]] ], {n, 0, z}] (* A241510 *)
CROSSREFS
Sequence in context: A050822 A187494 A283843 * A099536 A374075 A345001
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 24 2014
STATUS
approved

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Last modified July 21 05:28 EDT 2024. Contains 374463 sequences. (Running on oeis4.)