A309657 Sum of the odd parts in the partitions of n into 9 parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 8, 18, 24, 47, 60, 105, 136, 222, 290, 439, 574, 845, 1088, 1527, 1962, 2681, 3396, 4526, 5672, 7396, 9200, 11768, 14508, 18326, 22372, 27849, 33774, 41562, 50002, 60922, 72764, 87830, 104254, 124744, 147156, 174835, 205016

Offset

0,10

Links

Alois P. Heinz, Table of n, a(n) for n = 0..5000

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 mod 2) + p * (p mod 2) + o * (o mod 2) + m * (m mod 2) + l * (l mod 2) + k * (k mod 2) + j * (j mod 2) + i * (i mod 2) + (n-i-j-k-l-m-o-p-q) * ((n-i-j-k-l-m-o-p-q) mod 2).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[i * Mod[i, 2] + j * Mod[j, 2] + k * Mod[k, 2] + l * Mod[l, 2] + m * Mod[m, 2] + o * Mod[o, 2] + p * Mod[p, 2] + q * Mod[q, 2] + (n - i - j - k - l - m - o - p - q) * 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}]

Crossrefs

Sequence in context: A309656 A370882 A363327 * A296615 A340446 A063561

Adjacent sequences: A309654 A309655 A309656 * A309658 A309659 A309660

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 11 2019

Status

approved