A309658 Number of even parts in the partitions of n into 9 parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 5, 8, 15, 24, 39, 58, 90, 120, 170, 228, 310, 404, 537, 684, 886, 1116, 1415, 1756, 2198, 2690, 3315, 4022, 4895, 5876, 7083, 8426, 10056, 11880, 14055, 16484, 19366, 22560, 26317, 30488, 35340, 40712, 46932, 53788, 61674

Offset

0,12

Links

Table of n, a(n) for n=0..50.

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-1) mod 2) + ((p-1) mod 2) + ((o-1) mod 2) + ((m-1) mod 2) + ((l-1) mod 2) + ((k-1) mod 2) + ((j-1) mod 2) + ((i-1) mod 2) + ((n-i-j-k-l-m-o-p-q-1) mod 2).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[ Mod[i - 1, 2] + Mod[j - 1, 2] + Mod[k - 1, 2] + Mod[l - 1, 2] + Mod[m - 1, 2] + Mod[o - 1, 2] + Mod[p - 1, 2] + Mod[q - 1, 2] + Mod[n - i - j - k - l - m - o - p - q - 1, 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: A309551 A309625 A309630 * A309662 A066897 A078697

Adjacent sequences: A309655 A309656 A309657 * A309659 A309660 A309661

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 11 2019

Status

approved