A309628 Number of odd parts in the partitions of n into 8 parts.

0, 0, 0, 0, 0, 0, 0, 0, 8, 7, 14, 19, 32, 41, 64, 81, 118, 151, 208, 262, 354, 439, 572, 706, 900, 1094, 1368, 1650, 2032, 2431, 2950, 3500, 4206, 4950, 5882, 6879, 8104, 9412, 11000, 12699, 14736, 16920, 19500, 22276, 25530, 29020, 33072, 37432, 42450

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,{8}]],?(OddQ[#]&)],{n,0,50}] (* _Harvey P. Dale, Jul 31 2021 *)

Formula

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).