A309660 Number of odd parts in the partitions of n into 10 parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 9, 18, 25, 42, 55, 86, 111, 162, 210, 290, 371, 504, 635, 834, 1048, 1350, 1673, 2122, 2605, 3254, 3961, 4876, 5890, 7184, 8607, 10384, 12364, 14792, 17489, 20766, 24404, 28770, 33624, 39376, 45776, 53308, 61656, 71396

Offset: 0

Author

Wesley Ivan Hurt, Aug 11 2019

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to partitions

Programs

Mathematica

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

Formula

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).