cp's OEIS Frontend

A326036 Number of uniform complete integer partitions of n.

%I A326036 #4 Jun 04 2019 08:37:27
%S A326036 1,1,1,2,1,1,3,2,2,2,2,2,6,3,3,5,5,3,8,5,11,10,10,9,19,13,15,17,21,18,
%T A326036 35,26,39,40,50,50,77,63,84,88,113,103,146,132,171,180,212,214,292,
%U A326036 276,345,363,435,442,561,569,694,729,853,891,1108
%N A326036 Number of uniform complete integer partitions of n.
%C A326036 An integer partition of n is uniform if all parts appear with the same multiplicity, and complete if every nonnegative integer up to n is the sum of some submultiset.
%e A326036 The initial terms count the following partitions:
%e A326036    0: ()
%e A326036    1: (1)
%e A326036    2: (11)
%e A326036    3: (21)
%e A326036    3: (111)
%e A326036    4: (1111)
%e A326036    5: (11111)
%e A326036    6: (321)
%e A326036    6: (2211)
%e A326036    6: (111111)
%e A326036    7: (421)
%e A326036    7: (1111111)
%e A326036    8: (3311)
%e A326036    8: (11111111)
%e A326036    9: (222111)
%e A326036    9: (111111111)
%e A326036   10: (4321)
%e A326036   10: (1111111111)
%e A326036   11: (5321)
%e A326036   11: (11111111111)
%t A326036 sums[ptn_]:=sums[ptn]=If[Length[ptn]==1,ptn,Union@@(Join[sums[#],sums[#]+Total[ptn]-Total[#]]&/@Union[Table[Delete[ptn,i],{i,Length[ptn]}]])];
%t A326036 Table[Length[Select[IntegerPartitions[n],SameQ@@Length/@Split[#]&&Sort[sums[Sort[#]]]==Range[Total[#]]&]],{n,0,30}]
%Y A326036 Cf. A002033, A047966, A072774, A108917, A126796, A188431, A276024.
%Y A326036 Cf. A325781, A325791, A325988, A326020, A326035, A326037.
%K A326036 nonn
%O A326036 0,4
%A A326036 _Gus Wiseman_, Jun 04 2019