A309551 - OEIS

%I #8 Oct 04 2019 18:32:25

%S 0,0,0,0,0,0,0,1,2,5,8,15,24,32,44,62,82,108,140,179,226,284,348,427,

%T 520,623,744,887,1046,1228,1434,1668,1930,2225,2550,2917,3326,3772,

%U 4266,4817,5416,6076,6798,7586,8446,9383,10394,11498,12694,13979,15368

%N Number of even parts in the partitions of n into 6 parts.

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F a(n) = Sum_{m=1..floor(n/6)} Sum_{l=m..floor((n-m)/5)} Sum_{k=l..floor((n-l-m)/4)} Sum_{j=k..floor((n-k-l-m)/3)} Sum_(i=j..floor((n-j-k-l-m)/2)} (((i-1) mod 2) + ((j-1) mod 2) + ((k-1) mod 2) + ((l-1) mod 2) + ((m-1) mod 2) + ((n-i-j-k-l-m-1) mod 2)).

%t Table[Sum[Sum[Sum[Sum[Sum[ Mod[i - 1, 2] + Mod[j - 1, 2] + Mod[k - 1, 2] + Mod[l - 1, 2] + Mod[m - 1, 2] + Mod[n - i - j - k - l - m - 1, 2], {i, j, Floor[(n - j - k - l - m)/2]}], {j, k, Floor[(n - k - l - m)/3]}], {k, l, Floor[(n - l - m)/4]}], {l, m, Floor[(n - m)/5]}], {m, Floor[n/6]}], {n, 0, 50}]

%t Table[Count[Flatten[IntegerPartitions[n,{6}]],_?EvenQ],{n,0,50}] (* _Harvey P. Dale_, Oct 04 2019 *)

%K nonn

%O 0,9

%A _Wesley Ivan Hurt_, Aug 07 2019