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%I #10 Sep 08 2019 10:12:49
%S 0,0,0,0,0,2,2,6,6,14,18,32,38,62,72,104,122,170,200,264,302,388,444,
%T 554,628,768,866,1036,1160,1376,1532,1788,1976,2280,2518,2880,3160,
%U 3590,3920,4410,4802,5374,5838,6492,7018,7766,8378,9224,9922,10878,11674
%N Sum of the even parts appearing among the largest parts of 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)} (n-i-j-k) * ((n-i-j-k-1) 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) | 6 14 18 32 38 ...
%e --------------------------------------------------------------------------
%e - _Wesley Ivan Hurt_, Sep 07 2019
%t Table[Sum[Sum[Sum[(n - i - j - k)*Mod[n - i - j - k - 1, 2], {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 50}]
%K nonn
%O 0,6
%A _Wesley Ivan Hurt_, Aug 17 2019