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Number of partitions of n into 3 parts where at least one part is even.
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%I #8 Oct 22 2021 20:58:28

%S 0,0,0,1,1,3,2,5,4,8,6,12,9,16,12,21,16,27,20,33,25,40,30,48,36,56,42,

%T 65,49,75,56,85,64,96,72,108,81,120,90,133,100,147,110,161,121,176,

%U 132,192,144,208,156,225,169,243,182,261,196,280,210,300,225,320,240,341,256,363

%N Number of partitions of n into 3 parts where at least one part is even.

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} (1-(i mod 2)*(j mod 2)*((n-i-j) mod 2)).

%t a[n_] := Sum[1 - Mod[i, 2] * Mod[j, 2] * Mod[n - i - j, 2], {j, 1, Floor[n/3]}, {i, j, Floor[(n - j)/2]}]; Array[a, 100] (* _Amiram Eldar_, Oct 22 2021 *)

%Y Cf. A069905.

%K nonn

%O 1,6

%A _Wesley Ivan Hurt_, Oct 21 2021