|
|
A340571
|
|
Number of partitions of n into 4 parts with at least one even part.
|
|
2
|
|
|
0, 0, 0, 0, 0, 1, 1, 3, 3, 6, 6, 11, 10, 18, 17, 27, 25, 39, 36, 54, 49, 72, 66, 94, 85, 120, 109, 150, 135, 185, 167, 225, 202, 270, 243, 321, 287, 378, 339, 441, 394, 511, 457, 588, 524, 672, 600, 764, 680, 864, 770, 972, 864, 1089, 969, 1215, 1079, 1350, 1200, 1495, 1326
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,8
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} (1 - (k mod 2) * (j mod 2) * (i mod 2) * ((n-i-j-k) mod 2)).
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+1) mod 2) + ((j+1) mod 2) + ((i+1) mod 2) + ((n-i-j-k+1) mod 2) ).
|
|
EXAMPLE
|
a(5) = 1; [2,1,1,1];
a(7) = 3; [4,1,1,1], [3,2,1,1], [2,2,2,1];
a(9) = 6; [6,1,1,1], [5,2,1,1], [4,3,1,1], [4,2,2,1], [3,3,2,1], [3,2,2,2].
|
|
MATHEMATICA
|
Table[Sum[Sum[Sum[1 - Mod[k, 2] Mod[j, 2] Mod[i, 2] Mod[n - i - k - j, 2], {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 100}]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|