A309628 - OEIS

%I #9 Aug 17 2021 18:58:48

%S 0,0,0,0,0,0,0,0,8,7,14,19,32,41,64,81,118,151,208,262,354,439,572,

%T 706,900,1094,1368,1650,2032,2431,2950,3500,4206,4950,5882,6879,8104,

%U 9412,11000,12699,14736,16920,19500,22276,25530,29020,33072,37432,42450

%N Number of odd parts in the partitions of n into 8 parts.

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

%F a(n) = Sum_{p=1..floor(n/8)} Sum_{o=p..floor((n-p)/7)} Sum_{m=o..floor((n-o-p)/6)} Sum_{l=m..floor((n-m-o-p)/5)} Sum_{k=l..floor((n-l-m-o-p)/4)} Sum_{j=k..floor((n-k-l-m-o-p)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p)/2)} (i mod 2) + (j mod 2) + (k mod 2) + (l mod 2) + (m mod 2) + (o mod 2) + (p mod 2) + ((n-i-j-k-l-m-o-p) mod 2).

%t Table[Count[Flatten[IntegerPartitions[n,{8}]],_?(OddQ[#]&)],{n,0,50}] (* _Harvey P. Dale_, Jul 31 2021 *)

%K nonn

%O 0,9

%A _Wesley Ivan Hurt_, Aug 10 2019