login
A241512
Number of partitions of n such that (number parts having multiplicity 1) is not a part and (number of parts > 1) is a part.
5
0, 0, 0, 0, 2, 1, 2, 4, 4, 4, 5, 8, 9, 10, 13, 14, 21, 24, 31, 41, 52, 67, 89, 110, 134, 182, 219, 280, 337, 429, 523, 640, 785, 959, 1168, 1416, 1714, 2083, 2482, 2971, 3596, 4282, 5103, 6079, 7236, 8555, 10176, 11958, 14129, 16668, 19545, 22949, 26939
OFFSET
0,5
FORMULA
a(n) + A241511(n) + A241513(n) = A241515(n) for n >= 0.
EXAMPLE
a(6) counts these 2 partitions: 51, 2211.
MATHEMATICA
z = 30; 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, Length[p] - Count[p, 1]]], {n, 0, z}] (* A241511 *)
Table[Count[f[n], p_ /; ! MemberQ[p, u[p]] && MemberQ[p, Length[p] - Count[p, 1]] ], {n, 0, z}] (* A241512 *)
Table[Count[f[n], p_ /; MemberQ[p, u[p]] && ! MemberQ[p, Length[p] - Count[p, 1]] ], {n, 0, z}] (* A241513 *)
Table[Count[f[n], p_ /; ! MemberQ[p, u[p]] && ! MemberQ[p, Length[p] - Count[p, 1]] ], {n, 0, z}] (* A241514 *)
Table[Count[f[n], p_ /; MemberQ[p, u[p]] || MemberQ[p, Length[p] - Count[p, 1]] ], {n, 0, z}] (* A241515 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 24 2014
STATUS
approved