A309662 Number of even parts in the partitions of n into 10 parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 5, 8, 15, 24, 39, 58, 90, 130, 179, 246, 335, 446, 592, 770, 997, 1278, 1625, 2046, 2569, 3194, 3950, 4856, 5943, 7226, 8756, 10548, 12661, 15134, 18016, 21360, 25256, 29744, 34924, 40872, 47704, 55504, 64421, 74554

Offset

0,13

Links

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

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-1) mod 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-r-1) mod 2).

Mathematica

Table[Sum[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[r - 1, 2] + Mod[n - i - j - k - l - m - o - p - q - r - 1, 2], {i, j, Floor[(n - j - k - l - m - o - p - q - r)/2]}], {j, k, Floor[(n - k - l - m - o - p - q - r)/3]}], {k, l, Floor[(n - l - m - o - p - q - r)/4]}], {l, m, Floor[(n - m - o - p - q - r)/5]}], {m, o, Floor[(n - o - p - q - r)/6]}], {o, p, Floor[(n - p - q - r)/7]}], {p, q, Floor[(n - q - r)/8]}], {q, r, Floor[(n - r)/9]}], {r, Floor[n/10]}], {n, 0, 80}]

Crossrefs

Sequence in context: A309625 A309630 A309658 * A066897 A078697 A066629

Adjacent sequences: A309659 A309660 A309661 * A309663 A309664 A309665

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 11 2019

Status

approved