A309660 - OEIS

%I #13 Jul 26 2021 14:45:59

%S 0,0,0,0,0,0,0,0,0,0,10,9,18,25,42,55,86,111,162,210,290,371,504,635,

%T 834,1048,1350,1673,2122,2605,3254,3961,4876,5890,7184,8607,10384,

%U 12364,14792,17489,20766,24404,28770,33624,39376,45776,53308,61656,71396

%N Number of odd parts in the partitions of n into 10 parts.

%H Alois P. Heinz, <a href="/A309660/b309660.txt">Table of n, a(n) for n = 0..10000</a>

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

%F a(n) = Sum_{r=1..floor(n/10)} Sum_{q=r..floor((n-r)/9)} Sum_{p=q..floor((n-q-r)/8)} Sum_{o=p..floor((n-p-q-r)/7)} Sum_{m=o..floor((n-o-p-q-r)/6)} Sum_{l=m..floor((n-m-o-p-q-r)/5)} Sum_{k=l..floor((n-l-m-o-p-q-r)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q-r)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q-r)/2)} (r mod 2) + (q mod 2) + (p mod 2) + (o mod 2) + (m mod 2) + (l mod 2) + (k mod 2) + (j mod 2) + (i mod 2) + ((n-i-j-k-l-m-o-p-q-r) mod 2).

%t Table[Count[Flatten[IntegerPartitions[n,{10}]],_?OddQ],{n,0,50}] (* _Harvey P. Dale_, Jul 24 2021 *)

%K nonn,easy

%O 0,11

%A _Wesley Ivan Hurt_, Aug 11 2019