A308929 Sum of the fifth largest parts in the partitions of n into 7 parts.

0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 8, 13, 19, 27, 38, 54, 73, 101, 133, 177, 230, 298, 380, 485, 608, 762, 944, 1165, 1423, 1738, 2101, 2534, 3035, 3625, 4300, 5095, 5996, 7043, 8231, 9598, 11142, 12910, 14893, 17148, 19674, 22529, 25709, 29295, 33267

Offset

0,10

Links

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

Index entries for sequences related to partitions

Formula

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

a(n) = A308926(n) - A308927(n) - A308928(n) - A308930(n) - A308931(n) - A308932(n) - A308933(n).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[l, {i, j, Floor[(n - j - k - l - m - o)/2]}], {j, k, Floor[(n - k - l - m - o)/3]}], {k, l, Floor[(n - l - m - o)/4]}], {l, m, Floor[(n - m - o)/5]}], {m, o, Floor[(n - o)/6]}], {o, Floor[n/7]}], {n, 0, 50}]
Table[Total[IntegerPartitions[n, {7}][[;; , 5]]], {n, 0, 50}] (* Harvey P. Dale, May 10 2026 *)

Crossrefs

Cf. A026813, A308926, A308927, A308928, A308930, A308931, A308932, A308933.

Sequence in context: A355513 A281967 A178741 * A308994 A326469 A326594

Adjacent sequences: A308926 A308927 A308928 * A308930 A308931 A308932

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 30 2019

Status

approved