A309656 Number of odd parts in the partitions of n into 9 parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 8, 16, 22, 37, 48, 75, 96, 140, 180, 249, 316, 429, 536, 703, 876, 1125, 1382, 1746, 2122, 2636, 3184, 3898, 4668, 5662, 6724, 8065, 9522, 11320, 13272, 15660, 18246, 21370, 24770, 28812, 33218, 38425, 44076, 50692, 57900, 66254

Offset: 0

Author

Wesley Ivan Hurt, Aug 11 2019

Keywords

• nonn

Links

• Index entries for sequences related to partitions

Programs

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Mod[i, 2] + Mod[j, 2] + Mod[k, 2] + Mod[l, 2] + Mod[m, 2] + Mod[o, 2] + Mod[p, 2] + Mod[q, 2] + Mod[n - i - j - k - l - m - o - p - q, 2], {i, j, Floor[(n - j - k - l - m - o - p - q)/2]}], {j, k, Floor[(n - k - l - m - o - p - q)/3]}], {k, l, Floor[(n - l - m - o - p - q)/4]}], {l, m, Floor[(n - m - o - p - q)/5]}], {m, o, Floor[(n - o - p - q)/6]}], {o, p, Floor[(n - p - q)/7]}], {p, q, Floor[(n - q)/8]}], {q, Floor[n/9]}], {n, 0, 50}]

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 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) mod 2).