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

0,7

Links

Table of n, a(n) for n=0..59.

Index entries for sequences related to partitions

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)).

Example

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]).

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}]

Crossrefs

Cf. A026810, A340571.

Sequence in context: A368482 A105799 A347462 * A102463 A242110 A371069

Adjacent sequences: A340586 A340587 A340588 * A340590 A340591 A340592

Keyword

nonn

Author

Wesley Ivan Hurt, Jan 12 2021

Status

approved