A340589 - OEIS

%I #5 Jan 12 2021 21:33:30

%S 0,0,0,0,1,1,2,3,4,6,8,11,13,18,20,27,29,39,41,54,55,72,73,94,93,120,

%T 118,150,146,185,179,225,215,270,258,321,304,378,357,441,414,511,479,

%U 588,548,672,626,764,708,864,800,972,897,1089,1004,1215,1116,1350,1240,1495

%N Number of partitions of n into 4 parts with at least one odd part.

%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)} sign((k mod 2) + (j mod 2) + (i mod 2) + ((n-i-j-k) mod 2)).

%e a(7) = 3; [4,1,1,1], [3,2,1,1], [2,2,2,1].

%e a(8) = 4; [5,1,1,1], [4,2,1,1], [3,3,1,1], [3,2,2,1], (not [2,2,2,2]).

%t Table[Sum[Sum[Sum[Sign[Mod[k, 2] + Mod[j, 2] + Mod[i, 2] + 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}]

%Y Cf. A026810, A340571.

%K nonn

%O 0,7

%A _Wesley Ivan Hurt_, Jan 12 2021