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A309632
Sum of the even parts of the partitions of n into 8 parts.
0
0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 12, 18, 38, 60, 104, 152, 232, 324, 472, 642, 896, 1194, 1626, 2112, 2794, 3590, 4644, 5866, 7466, 9300, 11646, 14344, 17716, 21588, 26374, 31822, 38462, 46034, 55130, 65440, 77726, 91604, 107990, 126434, 148006, 172238
OFFSET
0,10
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 * ((i-1) mod 2) + j * ((j-1) mod 2) + k * ((k-1) mod 2) + l * ((l-1) mod 2) + m * ((m-1) mod 2) + o * ((o-1) mod 2) + p * ((p-1) mod 2) + (n-i-j-k-l-m-o-p) * ((n-i-j-k-l-m-o-p-1) mod 2).
MATHEMATICA
Table[Total[Select[Flatten[IntegerPartitions[n, {8}]], EvenQ]], {n, 0, 50}] (* Harvey P. Dale, Aug 20 2023 *)
CROSSREFS
Sequence in context: A309547 A309552 A309626 * A309659 A309664 A024872
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Aug 10 2019
STATUS
approved