The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A239945

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A239945

Number of partitions of n containing the number of distinct parts as a part.
(history; published version)

#5 by Bruno Berselli at Thu Apr 03 03:40:11 EDT 2014

STATUS

proposed

approved

#4 by Clark Kimberling at Tue Apr 01 09:04:29 EDT 2014

STATUS

editing

proposed

#3 by Clark Kimberling at Sun Mar 30 16:16:36 EDT 2014

NAME

allocated for Clark KimberlingNumber of partitions of n containing the number of distinct parts as a part.

DATA

0, 1, 1, 2, 2, 4, 5, 7, 10, 14, 19, 24, 35, 43, 61, 74, 100, 127, 165, 207, 268, 330, 423, 528, 653, 822, 1012, 1247, 1535, 1898, 2296, 2823, 3432, 4161, 5025, 6109, 7311, 8840, 10578, 12680, 15157, 18102, 21496, 25612, 30402, 35957, 42564, 50288, 59259

OFFSET

0,4

FORMULA

a(n) + A239946(n) = A000041(n) for n >= 0.

EXAMPLE

a(9) counts these 14 partitions: 72, 531, 522, 432, 4311, 3321, 3222, 32211, 321111, 22221, 222111, 2211111, 21111111, 111111111.

MATHEMATICA

z = 55; d[p_] := d[p] = Length[DeleteDuplicates[p]];

t = Table[Count[IntegerPartitions[n], p_ /; MemberQ[p, d[p]]], {n, 0, z}]

(* A239945 *)

Table[PartitionsP[n] - t[[n + 1]], {n, 0, z}] (* A239946 *)

CROSSREFS

Cf. A239946.

KEYWORD

allocated

nonn,easy

AUTHOR

Clark Kimberling, Mar 30 2014

STATUS

approved

editing

#2 by Clark Kimberling at Sat Mar 29 20:19:04 EDT 2014

KEYWORD

allocating

allocated

#1 by Clark Kimberling at Sat Mar 29 20:19:04 EDT 2014

NAME

allocated for Clark Kimberling

KEYWORD

allocating

STATUS

approved