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A340589
Number of partitions of n into 4 parts with at least one odd part.
1
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
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
Sequence in context: A368482 A105799 A347462 * A102463 A242110 A371069
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jan 12 2021
STATUS
approved