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

0,11

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Index entries for sequences related to partitions

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).

Mathematica

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

Crossrefs

Sequence in context: A360382 A284518 A369603 * A341821 A184959 A309661

Adjacent sequences: A309657 A309658 A309659 * A309661 A309662 A309663

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Aug 11 2019

Status

approved