A308932 Sum of the second largest parts in the partitions of n into 7 parts.

0, 0, 0, 0, 0, 0, 0, 1, 1, 3, 5, 10, 15, 27, 39, 61, 87, 128, 175, 249, 331, 450, 590, 779, 998, 1292, 1628, 2063, 2567, 3198, 3923, 4827, 5854, 7106, 8538, 10253, 12197, 14516, 17126, 20197, 23658, 27683, 32197, 37422, 43247, 49931, 57382, 65865, 75275

Offset: 0

Author

Wesley Ivan Hurt, Jun 30 2019

Keywords

• nonn

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A026813, A308926, A308927, A308928, A308929, A308930, A308931, A308933.

Programs

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[i, {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}]

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)} i.

a(n) = A308926(n) - A308927(n) - A308928(n) - A308929(n) - A308930(n) - A308931(n) - A308933(n).