A326471 Sum of the third largest parts of the partitions of n into 9 parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 7, 11, 19, 28, 44, 65, 94, 132, 190, 258, 355, 478, 640, 840, 1107, 1426, 1842, 2348, 2979, 3742, 4699, 5828, 7219, 8875, 10874, 13231, 16072, 19380, 23330, 27932, 33347, 39626, 46999, 55465, 65332, 76659, 89742, 104684

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)} j.

a(n) = A326464(n) - A326465(n) - A326466(n) - A326467(n) - A326468(n) - A326469(n) - A326470(n) - A326472(n) - A326473(n).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[j, {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

Cf. A026815, A326464, A326465, A326466, A326467, A326468, A326469, A326470, A326472, A326473.

Sequence in context: A325546 A308931 A308996 * A326596 A170804 A024622

Adjacent sequences: A326468 A326469 A326470 * A326472 A326473 A326474

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 10 2019

Status

approved