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A340571 Number of partitions of n into 4 parts with at least one even part.

%I A340571 #7 Jan 12 2021 21:33:20
%S A340571 0,0,0,0,0,1,1,3,3,6,6,11,10,18,17,27,25,39,36,54,49,72,66,94,85,120,
%T A340571 109,150,135,185,167,225,202,270,243,321,287,378,339,441,394,511,457,
%U A340571 588,524,672,600,764,680,864,770,972,864,1089,969,1215,1079,1350,1200,1495,1326
%N A340571 Number of partitions of n into 4 parts with at least one even part.
%H A340571 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A340571 a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} (1 - (k mod 2) * (j mod 2) * (i mod 2) * ((n-i-j-k) mod 2)).
%F A340571 a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} sign( ((k+1) mod 2) + ((j+1) mod 2) + ((i+1) mod 2) + ((n-i-j-k+1) mod 2) ).
%e A340571 a(5) = 1; [2,1,1,1];
%e A340571 a(7) = 3; [4,1,1,1], [3,2,1,1], [2,2,2,1];
%e A340571 a(9) = 6; [6,1,1,1], [5,2,1,1], [4,3,1,1], [4,2,2,1], [3,3,2,1], [3,2,2,2].
%t A340571 Table[Sum[Sum[Sum[1 - Mod[k, 2] Mod[j, 2] Mod[i, 2] Mod[n - i - k - j, 2], {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 100}]
%Y A340571 Cf. A026810, A340589.
%K A340571 nonn
%O A340571 0,8
%A A340571 _Wesley Ivan Hurt_, Jan 11 2021