A308927 Sum of the smallest parts in the partitions of n into 7 parts.

0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 11, 16, 22, 30, 41, 54, 72, 93, 121, 153, 194, 242, 302, 372, 457, 557, 675, 812, 975, 1162, 1381, 1632, 1924, 2254, 2636, 3068, 3562, 4119, 4752, 5463, 6265, 7162, 8170, 9293, 10549, 11942, 13496, 15211, 17115, 19214

Offset

0,10

Links

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

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)} o.

a(n) = A308926(n) - A308928(n) - A308929(n) - A308930(n) - A308931(n) - A308932(n) - A308933(n).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[o, {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}]

Crossrefs

Cf. A026813, A308926, A308928, A308929, A308930, A308931, A308932, A308933.

Sequence in context: A239054 A241725 A022480 * A366850 A024791 A178240

Adjacent sequences: A308924 A308925 A308926 * A308928 A308929 A308930

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 30 2019

Status

approved