A309661 Sum of the odd parts in the partitions of n into 10 parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 9, 20, 27, 52, 67, 116, 151, 244, 320, 480, 631, 924, 1199, 1676, 2172, 2966, 3791, 5054, 6405, 8374, 10501, 13472, 16762, 21244, 26183, 32714, 40034, 49500, 60081, 73554, 88664, 107582, 128818, 155000, 184456, 220400

Offset

0,11

Links

Table of n, a(n) for n=0..46.

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

Mathematica

Table[Sum[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] + r * Mod[r, 2] + (n - i - j - k - l - m - o - p - q - r) * Mod[n - i - j - k - l - m - o - p - q - r, 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, 50}]

Crossrefs

Sequence in context: A309660 A341821 A184959 * A003568 A305196 A099642

Adjacent sequences: A309658 A309659 A309660 * A309662 A309663 A309664

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 11 2019

Status

approved