A309622 Number of odd parts in the partitions of n into 7 parts.

0, 0, 0, 0, 0, 0, 0, 7, 6, 12, 16, 27, 34, 53, 66, 97, 122, 168, 208, 281, 342, 443, 536, 678, 812, 1008, 1196, 1462, 1722, 2072, 2420, 2885, 3344, 3937, 4538, 5297, 6064, 7022, 7994, 9190, 10412, 11886, 13400, 15215, 17074, 19274, 21544, 24204, 26946, 30137

Offset: 0

Author

Wesley Ivan Hurt, Aug 10 2019

Keywords

• nonn

Links

• Index entries for sequences related to partitions

Programs

Mathematica

Table[Count[Flatten[IntegerPartitions[n,{7}]],?OddQ],{n,0,50}] (* _Harvey P. Dale, Feb 28 2020 *)

Formula

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 mod 2) + (m mod 2) + (l mod 2) + (k mod 2) + (j mod 2) + (i mod 2) + ((n-i-j-k-l-m-o) mod 2).