A308990 Sum of the smallest parts in the partitions of n into 8 parts.

0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 11, 15, 23, 30, 42, 55, 75, 96, 127, 161, 209, 260, 330, 407, 509, 621, 765, 925, 1128, 1350, 1627, 1934, 2310, 2725, 3227, 3782, 4447, 5178, 6044, 7000, 8122, 9355, 10791, 12370, 14196, 16196, 18494, 21012, 23887

Offset

0,11

Links

Table of n, a(n) for n=0..52.

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)} p.

a(n) = A308989(n) - A308991(n) - A308992(n) - A308994(n) - A308995(n) - A308996(n) - A308997(n) - A308998(n).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[p, {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, A308991, A308992, A308994, A308995, A308996, A308997, A308998.

Sequence in context: A236102 A241726 A353723 * A321142 A336106 A366845

Adjacent sequences: A308987 A308988 A308989 * A308991 A308992 A308993

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 04 2019

Status

approved