A309659 Sum of the even parts in the partitions of n into 9 parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 12, 18, 38, 60, 104, 152, 250, 340, 506, 688, 980, 1302, 1806, 2344, 3156, 4060, 5332, 6756, 8740, 10924, 13876, 17182, 21522, 26366, 32646, 39616, 48494, 58418, 70796, 84616, 101714, 120700, 143904, 169730, 200888, 235512

Offset

0,11

Comments

All terms are even.

Links

Table of n, a(n) for n=0..47.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{q=1..floor(n/9)} Sum_{p=q..floor((n-q)/8)} Sum_{o=p..floor((n-p-q)/7)} Sum_{m=o..floor((n-o-p-q)/6)} Sum_{l=m..floor((n-m-o-p-q)/5)} Sum_{k=l..floor((n-l-m-o-p-q)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q)/2)} q * ((q-1) mod 2) + p * ((p-1) mod 2) + o * ((o-1) mod 2) + m * ((m-1) mod 2) + l * ((l-1) mod 2) + k * ((k-1) mod 2) + j * ((j-1) mod 2) + i * ((i-1) mod 2) + (n-i-j-k-l-m-o-p-q) * ((n-i-j-k-l-m-o-p-q-1) mod 2). [Corrected by Georg Fischer, Mar 11 2025]

Mathematica

Table[Total[Select[Flatten[IntegerPartitions[n, {9}]], EvenQ]], {n, 0, 50}] (* Harvey P. Dale, Nov 23 2025 *)

Crossrefs

Sequence in context: A309552 A309626 A309632 * A309664 A024872 A129021

Adjacent sequences: A309656 A309657 A309658 * A309660 A309661 A309662

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 11 2019

Status

approved