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A241506
Number of partitions of n such that (number parts having multiplicity 1) is a part and (number of 1s) is a part.
10
0, 1, 0, 1, 1, 1, 2, 3, 5, 7, 11, 12, 17, 25, 32, 40, 54, 73, 95, 123, 152, 195, 252, 319, 395, 491, 624, 759, 951, 1167, 1446, 1767, 2147, 2631, 3212, 3881, 4684, 5672, 6848, 8215, 9825, 11809, 14070, 16818, 19957, 23737, 28169, 33377, 39357, 46546, 54814
OFFSET
0,7
FORMULA
a(n) + A241507(n) + A241508(n) = A241510(n) for n >= 0.
EXAMPLE
a(6) counts these 2 partitions: 51, 2211.
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