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A348542
Number of partitions of n into 3 parts where at least one part is even.
0
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
1,6
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)).
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 *)
CROSSREFS
Cf. A069905.
Sequence in context: A194078 A169752 A095720 * A318460 A276582 A240729
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Oct 21 2021
STATUS
approved