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A241507
Number of partitions of n such that (number parts having multiplicity 1) is not a part and (number of 1s) is a part.
5
0, 0, 0, 0, 1, 1, 2, 2, 3, 3, 5, 7, 12, 11, 19, 23, 35, 35, 53, 59, 90, 102, 138, 156, 220, 259, 331, 402, 515, 607, 771, 912, 1169, 1363, 1699, 2011, 2513, 2941, 3603, 4255, 5230, 6096, 7438, 8695, 10546, 12344, 14797, 17301, 20760, 24186, 28783, 33566
OFFSET
0,7
FORMULA
a(n) + A241506(n) + A241508(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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 24 2014
STATUS
approved