A308994 Sum of the fifth largest parts in the partitions of n into 8 parts.

0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 8, 13, 19, 29, 40, 58, 79, 111, 148, 201, 264, 349, 449, 583, 739, 943, 1181, 1482, 1833, 2273, 2780, 3405, 4126, 5002, 6006, 7215, 8593, 10235, 12101, 14300, 16795, 19713, 23003, 26825, 31124, 36083, 41638, 48012

Offset

0,11

Links

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

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)} l.

a(n) = A308989(n) - A308990(n) - A308991(n) - A308992(n) - A308995(n) - A308996(n) - A308997(n) - A308998(n).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[l, {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, A308992, A308995, A308996, A308997, A308998.

Sequence in context: A281967 A178741 A308929 * A326469 A326594 A045842

Adjacent sequences: A308991 A308992 A308993 * A308995 A308996 A308997

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 04 2019

Status

approved