A308931 Sum of the third largest parts in the partitions of n into 7 parts.

0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 7, 11, 19, 28, 42, 61, 88, 121, 171, 228, 307, 405, 531, 682, 880, 1111, 1403, 1750, 2174, 2670, 3281, 3983, 4827, 5807, 6965, 8291, 9861, 11641, 13718, 16080, 18804, 21881, 25423, 29392, 33921, 39001, 44753, 51163, 58411

Offset

0,10

Links

Table of n, a(n) for n=0..49.

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)} j.

a(n) = A308926(n) - A308927(n) - A308928(n) - A308929(n) - A308930(n) - A308932(n) - A308933(n).

Mathematica

Table[Total[IntegerPartitions[n, {7}][[All, 3]]], {n, 0, 50}] (* Harvey P. Dale, Aug 15 2020 *)

Crossrefs

Cf. A026813, A308926, A308927, A308928, A308929, A308930, A308932, A308933.

Sequence in context: A357210 A308871 A325546 * A308996 A326471 A326596

Adjacent sequences: A308928 A308929 A308930 * A308932 A308933 A308934

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 30 2019

Status

approved