A340589 Number of partitions of n into 4 parts with at least one odd part.

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, 118, 150, 146, 185, 179, 225, 215, 270, 258, 321, 304, 378, 357, 441, 414, 511, 479, 588, 548, 672, 626, 764, 708, 864, 800, 972, 897, 1089, 1004, 1215, 1116, 1350, 1240, 1495

Offset: 0

Author

Wesley Ivan Hurt, Jan 12 2021

Keywords

• nonn

Examples

			a(7) = 3; [4,1,1,1], [3,2,1,1], [2,2,2,1].
a(8) = 4; [5,1,1,1], [4,2,1,1], [3,3,1,1], [3,2,2,1], (not [2,2,2,2]).
		

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A026810, A340571.

Programs

Mathematica

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}]

Formula

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)).