A348542 Number of partitions of n into 3 parts where at least one part is even.

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, 65, 49, 75, 56, 85, 64, 96, 72, 108, 81, 120, 90, 133, 100, 147, 110, 161, 121, 176, 132, 192, 144, 208, 156, 225, 169, 243, 182, 261, 196, 280, 210, 300, 225, 320, 240, 341, 256, 363

Offset: 1

Author

Wesley Ivan Hurt, Oct 21 2021

Keywords

• nonn

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A069905.

Programs

Mathematica

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 *)

Formula

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)).