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

1,6

Links

Table of n, a(n) for n=1..66.

Index entries for sequences related to partitions

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

Adjacent sequences: A348539 A348540 A348541 * A348543 A348544 A348545

Keyword

nonn

Author

Wesley Ivan Hurt, Oct 21 2021

Status

approved