A309625 - OEIS

%I #9 Dec 23 2021 03:56:17

%S 0,0,0,0,0,0,0,0,1,2,5,8,15,24,39,50,74,98,135,174,232,292,381,470,

%T 595,728,904,1086,1330,1582,1906,2246,2676,3126,3687,4272,4989,5746,

%U 6657,7610,8754,9954,11373,12862,14608,16440,18573,20806,23384,26094,29194

%N Number of even parts in the partitions of n into 7 parts.

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

%F a(n) = Sum_{o=1..floor(n/7)} Sum_{m=o..floor((n-o)/6)} Sum_{l=m..floor((n-m-o)/5)} Sum_{k=l..floor((n-l-m-o)/4)} Sum_{j=k..floor((n-k-l-m-o)/3} Sum_{i=j..floor((n-j-k-l-m-o)/2)} ((o-1) mod 2) + ((m-1) mod 2) + ((l-1) mod 2) + ((k-1) mod 2) + ((j-1) mod 2) + ((i-1) mod 2) + ((n-i-j-k-l-m-o-1) mod 2).

%t Table[Count[Flatten[IntegerPartitions[n,{7}]],_?EvenQ],{n,0,50}] (* _Harvey P. Dale_, Dec 18 2021 *)

%K nonn

%O 0,10

%A _Wesley Ivan Hurt_, Aug 10 2019