A326588 Sum of all the parts in the partitions of n into 10 parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 11, 24, 39, 70, 105, 176, 255, 396, 570, 840, 1155, 1650, 2231, 3072, 4100, 5512, 7209, 9520, 12267, 15900, 20243, 25824, 32472, 40936, 50925, 63396, 78144, 96292, 117585, 143600, 173922, 210546, 253184, 304128, 363150

Offset

0,11

Links

Table of n, a(n) for n=0..45.

Index entries for sequences related to partitions

Formula

a(n) = 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)} 1.

a(n) = n * A026816(n).

a(n) = A326589(n) + A326590(n) + A326591(n) + A326592(n) + A326593(n) + A326594(n) + A326595(n) + A326596(n) + A326597(n) + A326598(n).

Mathematica

Table[n * Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[1, {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

Cf. A026816, A326589, A326590, A326591, A326592, A326593, A326594, A326595, A326596, A326597, A326598.

Sequence in context: A367354 A326627 A309486 * A309357 A051803 A082517

Adjacent sequences: A326585 A326586 A326587 * A326589 A326590 A326591

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 13 2019

Status

approved