A308992 Sum of the sixth largest parts in the partitions of n into 8 parts.

0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 12, 17, 26, 35, 50, 67, 94, 123, 167, 216, 285, 362, 469, 589, 749, 931, 1165, 1431, 1771, 2152, 2630, 3171, 3836, 4585, 5497, 6521, 7753, 9134, 10775, 12615, 14784, 17202, 20030, 23182, 26837, 30897, 35581, 40769

Offset

0,11

Links

Table of n, a(n) for n=0..51.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{p=1..floor(n/8)} Sum_{o=p..floor((n-p)/7)} Sum_{m=o..floor((n-o-p)/6)} Sum_{l=m..floor((n-m-o-p)/5)} Sum_{k=l..floor((n-l-m-o-p)/4)} Sum_{j=k..floor((n-k-l-m-o-p)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p)/2)} m.

a(n) = A308989(n) - A308990(n) - A308991(n) - A308994(n) - A308995(n) - A308996(n) - A308997(n) - A308998(n).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[m, {i, j, Floor[(n - j - k - l - m - o - p)/2]}], {j, k, Floor[(n - k - l - m - o - p)/3]}], {k, l, Floor[(n - l - m - o - p)/4]}], {l, m, Floor[(n - m - o - p)/5]}], {m, o, Floor[(n - o - p)/6]}], {o, p, Floor[(n - p)/7]}], {p, Floor[n/8]}], {n, 0, 50}]

Crossrefs

Cf. A026814, A308989, A308990, A308991, A308994, A308995, A308996, A308997, A308998.

Sequence in context: A027959 A060730 A308928 * A326468 A326593 A123569

Adjacent sequences: A308989 A308990 A308991 * A308993 A308994 A308995

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 04 2019

Status

approved