A308926 - OEIS

%I #8 Jul 02 2019 11:19:46

%S 0,0,0,0,0,0,0,7,8,18,30,55,84,143,210,315,448,646,882,1235,1640,2205,

%T 2882,3772,4824,6200,7800,9828,12208,15138,18540,22723,27520,33297,

%U 39950,47845,56844,67488,79534,93600,109520,127920,148638,172473,199144,229590

%N Sum of all the parts in the partitions of n into 7 parts.

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F a(n) = 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)} 1.

%F a(n) = n * A026813(n).

%F a(n) = A308927(n) + A308928(n) + A308929(n) + A308930(n) + A308931(n) + A308932(n) + A308933(n).

%t Table[n*Sum[Sum[Sum[Sum[Sum[Sum[1, {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}]

%Y Cf. A026813, A308927, A308928, A308929, A308930, A308931, A308932, A308933.

%K nonn

%O 0,8

%A _Wesley Ivan Hurt_, Jun 30 2019