A284609 - OEIS

%I #15 Aug 04 2019 19:14:25

%S 0,0,1,1,0,0,4,4,0,0,9,12,0,0,25,30,0,0,56,70,0,0,132,165,0,0,270,330,

%T 0,0,594,704,0,0,1140,1380,0,0,2268,2688,0,0,4256,4984,0,0,8008,9394,

%U 0,0,14342,16665,0,0,25920,29970,0,0,45056,52096

%N Number of partitions of n such that the (sum of all odd parts) = floor(n/2).

%C Consequently the sum of all even parts is ceiling(n/2). Therefore, a(4n + 1) = a(4n + 2) = 0. - _David A. Corneth_, Apr 02 2017

%e a(8) counts these 4 partitions: 431, 3221, 32111, 311111.

%t Table[p = IntegerPartitions[n];   Length[Select[

%t    Table[Total[Select[DeleteDuplicates[p[[k]]], EvenQ]], {k,

%t      Length[p]}], # == Floor[n/2] &]], {n, 60}] (* _Peter J. C. Moses_, Mar 29 2017 *)

%Y Cf. A284608, A284611.

%K nonn,easy

%O 1,7

%A _Clark Kimberling_, Mar 30 2017