The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A114639 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A114639

Number of partitions of n such that the set of parts and the set of multiplicities of parts are disjoint.
(history; published version)

#17 by Alois P. Heinz at Tue Jul 07 06:05:58 EDT 2020

STATUS

editing

approved

#16 by Alois P. Heinz at Tue Jul 07 06:01:55 EDT 2020

CROSSREFS

Cf. A052335, A087153, A114640, A115584, A117144, A276429, A324572, A325130, A325131, A336032.

STATUS

approved

editing

#15 by Susanna Cuyler at Tue Apr 02 08:05:56 EDT 2019

STATUS

proposed

approved

#14 by Gus Wiseman at Tue Apr 02 04:46:26 EDT 2019

STATUS

editing

proposed

#13 by Gus Wiseman at Tue Apr 02 02:30:47 EDT 2019

COMMENTS

The Heinz numbers of these partitions are given by A325131. - Gus Wiseman, Apr 02 2019

EXAMPLE

From Gus Wiseman, Apr 02 2019: (Start)

The a(2) = 2 through a(9) = 7 partitions:

(2) (3) (4) (5) (6) (7) (8) (9)

(11) (111) (1111) (32) (33) (43) (44) (54)

(11111) (42) (52) (53) (63)

(222) (1111111) (62) (72)

(111111) (2222) (432)

(3311) (222111)

(11111111) (111111111)

(End)

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], Intersection[#, Length/@Split[#]]=={}&]], {n, 0, 30}] (* Gus Wiseman, Apr 02 2019 *)

CROSSREFS

Cf. A052335, A087153, A114640, A115584, A117144, A276429, A324572, A325130, A325131.

STATUS

approved

editing

#12 by Alois P. Heinz at Sun Feb 05 07:48:43 EST 2017

STATUS

reviewed

approved

#11 by Wesley Ivan Hurt at Sun Feb 05 07:42:51 EST 2017

STATUS

proposed

reviewed

#10 by Jean-François Alcover at Sun Feb 05 07:40:14 EST 2017

STATUS

editing

proposed

#9 by Jean-François Alcover at Sun Feb 05 07:40:09 EST 2017

MATHEMATICA

b[n_, i_, p_, m_] := b[n, i, p, m] = If[n == 0, 1, If[i<1, 0, b[n, i-1, p, Select[m, #<i&]] + Sum[If[i == j || MemberQ[m, i] || MemberQ[p, j], 0, b[n-i*j, i-1, Select[ p ~Union~ {i}, # <= n-i*j&], Select[m ~Union~ {j}, #<i&]]], {j, 1, n/i}]]]; a[n_] := b[n, n, {}, {}]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Feb 05 2017, after Alois P. Heinz *)

STATUS

approved

editing

#8 by Alois P. Heinz at Tue Aug 09 17:58:13 EDT 2016

STATUS

editing

approved