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%I #4 Jan 19 2021 21:28:03
%S 0,0,0,0,1,1,1,2,4,4,5,7,10,11,13,16,21,23,26,31,38,41,46,53,62,67,74,
%T 83,95,102,111,123,138,147,159,174,192,204,219,237,259,274,292,314,
%U 340,358,380,406,436,458,484,514,549,575,605,640,680,710,745,785,830,865,905,950,1001
%N Number of partitions of n into 4 parts whose 'middle' two parts have the same parity.
%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)} [(j mod 2) = (i mod 2)], where [ ] is the Iverson bracket.
%t Table[Sum[Sum[Sum[KroneckerDelta[Mod[i, 2], Mod[j, 2]], {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 80}]
%K nonn
%O 0,8
%A _Wesley Ivan Hurt_, Jan 19 2021
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