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A240674 Number of partitions p of n that are disjoint from their complement. 3
0, 2, 2, 2, 2, 4, 4, 8, 10, 10, 14, 18, 18, 26, 30, 36, 44, 60, 64, 82, 96, 114, 130, 164, 176, 222, 248, 296, 338, 406, 450, 550, 620, 726, 816, 968, 1074, 1270, 1418, 1648, 1836, 2150, 2382, 2758, 3080, 3534, 3942, 4538, 5034, 5778, 6416, 7312, 8136, 9258 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

First column of the array at A240181.

LINKS

Table of n, a(n) for n=1..54.

FORMULA

a(n) = 2*A114701(n), for n >= 1.

EXAMPLE

a(6) counts these 4 partitions:  6, 33, 222, 111111, of which the respective conjugates are 111111, 222, 33, 6.

MATHEMATICA

z = 30; p[n_, k_] := p[n, k] = IntegerPartitions[n][[k]]; c[p_] := c[p] = Table[Count[#, _?(# >= i &)], {i, First[#]}] &[p]; b[n_] := b[n] = Table[Intersection[p[n, k], c[p[n, k]]], {k, 1, PartitionsP[n]}]; Table[Count[Map[Length, b[n]], 0], {n, 1, z}] (* A240674 *)

Table[Count[Map[Length, b[n]], 1], {n, 1, z}]   (* A240675 *)

CROSSREFS

Cf. A240675, A114701, A240181.

Sequence in context: A010334 A010578 A328583 * A005866 A125584 A230447

Adjacent sequences:  A240671 A240672 A240673 * A240675 A240676 A240677

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 12 2014

STATUS

approved

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Last modified April 23 01:31 EDT 2021. Contains 343198 sequences. (Running on oeis4.)