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%I #9 Sep 08 2019 02:03:44
%S 0,0,0,0,4,3,8,9,22,26,50,59,100,114,168,197,284,329,438,504,660,748,
%T 946,1072,1322,1488,1794,2008,2408,2671,3130,3465,4024,4434,5100,5595,
%U 6384,6966,7866,8565,9630,10449,11648,12600,13992,15080,16652,17912,19684
%N Sum of the odd parts in the partitions of n into 4 parts.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} (i * (i mod 2) + j * (j mod 2) + k * (k mod 2) + (n-i-j-k) * ((n-i-j-k) mod 2)).
%e Figure 1: The partitions of n into 4 parts for n = 8, 9, ..
%e 1+1+1+9
%e 1+1+2+8
%e 1+1+3+7
%e 1+1+4+6
%e 1+1+1+8 1+1+5+5
%e 1+1+2+7 1+2+2+7
%e 1+1+1+7 1+1+3+6 1+2+3+6
%e 1+1+2+6 1+1+4+5 1+2+4+5
%e 1+1+3+5 1+2+2+6 1+3+3+5
%e 1+1+1+6 1+1+4+4 1+2+3+5 1+3+4+4
%e 1+1+1+5 1+1+2+5 1+2+2+5 1+2+4+4 2+2+2+6
%e 1+1+2+4 1+1+3+4 1+2+3+4 1+3+3+4 2+2+3+5
%e 1+1+3+3 1+2+2+4 1+3+3+3 2+2+2+5 2+2+4+4
%e 1+2+2+3 1+2+3+3 2+2+2+4 2+2+3+4 2+3+3+4
%e 2+2+2+2 2+2+2+3 2+2+3+3 2+3+3+3 3+3+3+3
%e --------------------------------------------------------------------------
%e n | 8 9 10 11 12 ...
%e --------------------------------------------------------------------------
%e a(n) | 22 26 50 59 100 ...
%e --------------------------------------------------------------------------
%e - _Wesley Ivan Hurt_, Sep 08 2019
%t Table[Sum[Sum[Sum[(i * Mod[i, 2] + j * Mod[j, 2] + k * Mod[k, 2] + (n - i - j - k) * Mod[n - i - j - k, 2]), {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 100}]
%K nonn
%O 0,5
%A _Wesley Ivan Hurt_, Aug 05 2019