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A241509
Number of partitions of n such that (number parts having multiplicity 1) is not a part and (number of 1s) is not a part.
5
1, 0, 2, 2, 3, 2, 4, 5, 9, 10, 16, 20, 27, 31, 48, 53, 72, 92, 118, 143, 186, 220, 288, 356, 434, 523, 675, 792, 989, 1205, 1469, 1754, 2165, 2565, 3133, 3752, 4498, 5345, 6496, 7629, 9126, 10869, 12890, 15212, 18114, 21220, 25163, 29611, 34783, 40756, 48058
OFFSET
0,3
FORMULA
a(n) + A241510(n) = A000041(n) for n >= 0.
EXAMPLE
a(6) counts these 4 partitions: 6, 33, 222, 111111.
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