A309622 - OEIS

%I #7 Feb 28 2020 16:04:00

%S 0,0,0,0,0,0,0,7,6,12,16,27,34,53,66,97,122,168,208,281,342,443,536,

%T 678,812,1008,1196,1462,1722,2072,2420,2885,3344,3937,4538,5297,6064,

%U 7022,7994,9190,10412,11886,13400,15215,17074,19274,21544,24204,26946,30137

%N Number of odd 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) = 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 mod 2) + (m mod 2) + (l mod 2) + (k mod 2) + (j mod 2) + (i mod 2) + ((n-i-j-k-l-m-o) mod 2).

%t Table[Sum[Sum[Sum[Sum[Sum[Sum[Mod[i, 2] + Mod[j, 2] + Mod[k, 2] + Mod[l, 2] + Mod[m, 2] + Mod[o, 2] + Mod[n - i - j - k - l - m - o, 2], {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}]

%t Table[Count[Flatten[IntegerPartitions[n,{7}]],_?OddQ],{n,0,50}] (* _Harvey P. Dale_, Feb 28 2020 *)

%K nonn

%O 0,8

%A _Wesley Ivan Hurt_, Aug 10 2019