cp's OEIS Frontend

A284619 Number of partitions of n such that the (sum of distinct even parts) >= n/2.

%I A284619 #10 Aug 14 2023 08:11:50
%S A284619 0,1,1,3,1,3,4,8,7,13,18,29,20,33,45,68,62,92,126,179,170,240,322,441,
%T A284619 387,530,699,934,883,1179,1537,2010,1924,2514,3235,4169,4094,5272,
%U A284619 6701,8521,7983,10149,12784,16074,15733,19770,24669,30726,29682,36968,45755
%N A284619 Number of partitions of n such that the (sum of distinct even parts) >= n/2.
%C A284619 The number of partitions of n such that (sum distinct even parts) = n/2 is A284617(n)-A284616(n) = A284619(n)-A284618(n) = 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 15, 0, 0, 0, 23, 0, 0, 0, 55, 0, 0, 0, 153, 0, 0, 0, 265,... (offset 1, nonzero for 4|n) - _R. J. Mathar_, Aug 14 2023
%e A284619 a(4) counts these 3 partitions: 4, 22, 211.
%t A284619 Table[p = IntegerPartitions[n];
%t A284619 Length[Select[Table[Total[Select[DeleteDuplicates[p[[k]]], EvenQ]], {k,
%t A284619      Length[p]}], # >= n/2 &]], {n, 54}]
%Y A284619 Cf. A284616, A284617, A284618.
%K A284619 nonn,easy
%O A284619 1,4
%A A284619 _Clark Kimberling_, Apr 02 2017