cp's OEIS Frontend

A114640 Number of partitions of n such that the set of parts and the set of multiplicities of parts are equal.

%I A114640 #15 Jul 07 2020 06:07:02
%S A114640 1,1,0,0,2,1,1,0,1,1,3,2,3,3,5,0,4,5,2,3,8,6,5,10,9,9,16,14,12,16,17,
%T A114640 10,17,15,16,19,35,17,34,37,40,31,54,36,60,61,58,63,88,58,88,87,91,84,
%U A114640 115,93,116,108,115,130,190,143,165,214,219,200,255,240
%N A114640 Number of partitions of n such that the set of parts and the set of multiplicities of parts are equal.
%C A114640 The Heinz numbers of these partitions are given by A109297. - _Gus Wiseman_, Apr 02 2019
%e A114640 From _Gus Wiseman_, Apr 02 2019: (Start)
%e A114640 The initial terms count the following integer partitions:
%e A114640    0: ()
%e A114640    1: (1)
%e A114640    4: (22)
%e A114640    4: (211)
%e A114640    5: (221)
%e A114640    6: (3111)
%e A114640    8: (41111)
%e A114640    9: (333)
%e A114640   10: (511111)
%e A114640   10: (3331)
%e A114640   10: (322111)
%e A114640   11: (332111)
%e A114640   11: (322211)
%e A114640   12: (6111111)
%e A114640   12: (4221111)
%e A114640   12: (33222)
%e A114640   13: (33322)
%e A114640   13: (333211)
%e A114640   13: (332221)
%e A114640   14: (71111111)
%e A114640   14: (52211111)
%e A114640   14: (4421111)
%e A114640   14: (4222211)
%e A114640   14: (333221)
%e A114640 (End)
%t A114640 Table[Length[Select[IntegerPartitions[n],Union[#]==Union[Length/@Split[#]]&]],{n,0,30}] (* _Gus Wiseman_, Apr 02 2019 *)
%Y A114640 Cf. A052335, A087153, A109297, A114639, A115584, A117144, A276429, A324572, A325132, A336031.
%K A114640 nonn
%O A114640 0,5
%A A114640 _Vladeta Jovovic_, Feb 18 2006
%E A114640 More terms from _Alois P. Heinz_, Aug 09 2016