cp's OEIS Frontend

A326357 a(n) = number of partitions of n that occur more than once among the condensed partitions of n; see A239312.

%I A326357 #10 Jul 01 2019 14:26:42
%S A326357 0,0,1,1,1,3,2,4,5,7,11,11,15,19,25,29,39,47,61,67,85,107,128,154,182,
%T A326357 219,264,310,366,441,514,608,705,836,974,1128,1312,1530,1776,2053,
%U A326357 2367,2735,3156,3598,4145,4745,5463,6204,7084,8068,9241,10455,11906,13488
%N A326357 a(n) = number of partitions of n that occur more than once among the condensed partitions of n; see A239312.
%e A326357 The partitions of 5 are [5], [4,1], [3,2], [3,1,1], [2,2,1], [2,1,1,1], [1,1,1,1,1], with respective condensations [5], [4,1], [3,2], [3,2], [4,1], [3,2], [5]; of these, three occur more than once, so that a(5) = 3.
%t A326357 p[n_] := IntegerPartitions[n];
%t A326357 m[n_] := Map[Split, p[n]];
%t A326357 t[n_, k_] := Map[Total, m[n][[k]]];
%t A326357 u[n_] := Table[Sort[t[n, k], Greater], {k, 1, Length[p[n]]}]
%t A326357 v[n_] := Tally[u[n]];
%t A326357 w[n_] := Length[Select[v[n], #[[2]] > 1 &] ];l
%t A326357 Table[w[n], {n, 1, 20}]
%Y A326357 Cf. A000009, A000041, A239312.
%K A326357 nonn,easy
%O A326357 0,6
%A A326357 _Clark Kimberling_, Jun 30 2019
%E A326357 More terms from _Alois P. Heinz_, Jun 30 2019