The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A239737 Number of partitions p of n such that the number of numbers having multiplicity 1 in p is a part or the number of numbers having multiplicity > 1 is a part. 6
 0, 1, 1, 2, 2, 5, 7, 10, 13, 21, 28, 38, 54, 77, 99, 137, 180, 236, 306, 398, 504, 644, 807, 1018, 1278, 1599, 1972, 2458, 3039, 3743, 4592, 5659, 6884, 8436, 10235, 12445, 15021, 18204, 21842, 26334, 31501, 37746, 44956, 53707, 63657, 75738, 89536, 106057 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Table of n, a(n) for n=0..47. FORMULA a(n) + A241417(n) = A000041(n) for n >= 0. EXAMPLE a(6) counts these 7 partitions: 42, 411, 321, 3111, 2211, 21111, 111111. MATHEMATICA z = 30; f[n_] := f[n] = IntegerPartitions[n]; u[p_] := Length[DeleteDuplicates[Select[p, Count[p, #] == &]]]; e[q_] := Length[DeleteDuplicates[Select[q, Count[q, #] > 1 &]]] Table[Count[f[n], p_ /; MemberQ[p, u[p]]], {n, 0, z}] (* A241413 *) Table[Count[f[n], p_ /; MemberQ[p, u[p]] && MemberQ[p, e[p]]], {n, 0, z}] (* A241414 *) Table[Count[f[n], p_ /; ! MemberQ[p, u[p]] && MemberQ[p, e[p]] ], {n, 0, z}] (* A241415 *) Table[Count[f[n], p_ /; MemberQ[p, u[p]] && ! MemberQ[p, e[p]] ], {n, 0, z}] (* A241416 *) Table[Count[f[n], p_ /; ! MemberQ[p, u[p]] && ! MemberQ[p, e[p]] ], {n, 0, z}] (* A241417 *) Table[Count[f[n], p_ /; MemberQ[p, u[p]] || MemberQ[p, e[p]] ], {n, 0, z}] (* A239737 *) CROSSREFS Cf. A241413, A241414, A241415, A241416, A241417, A000041. Sequence in context: A308842 A241761 A278388 * A262883 A308908 A259446 Adjacent sequences: A239734 A239735 A239736 * A239738 A239739 A239740 KEYWORD nonn,easy AUTHOR Clark Kimberling, Apr 23 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 4 22:44 EDT 2023. Contains 365888 sequences. (Running on oeis4.)