A241510 Number of partitions of n such that (number parts having multiplicity 1) is a part or (number of 1s) is a part.

0, 1, 0, 1, 2, 5, 7, 10, 13, 20, 26, 36, 50, 70, 87, 123, 159, 205, 267, 347, 441, 572, 714, 899, 1141, 1435, 1761, 2218, 2729, 3360, 4135, 5088, 6184, 7578, 9177, 11131, 13479, 16292, 19519, 23556, 28212, 33714, 40284, 48049, 57061, 67914, 80395, 95143

Offset

0,5

Links

Table of n, a(n) for n=0..47.

Formula

a(n) + A241509(n) = A000041(n) for n >= 0.

Example

a(6) counts these 7 partitions:  51, 42, 411, 321, 3111, 2211, 21111.

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

Cf. A241506, A241507, A241508, A241509.

Sequence in context: A094065 A073593 A364451 * A088947 A288209 A071113

Adjacent sequences: A241507 A241508 A241509 * A241511 A241512 A241513

Keyword

nonn,easy

Author

Clark Kimberling, Apr 24 2014

Status

approved