

A343399


Number of partitions of n into 3 distinct parts [r,s,t] such that r < s < t where at least 1 part does not divide any larger part.


0



0, 0, 0, 0, 0, 1, 0, 2, 2, 3, 4, 7, 5, 9, 11, 12, 14, 18, 18, 23, 23, 27, 32, 37, 35, 40, 46, 49, 53, 59, 60, 68, 71, 76, 83, 88, 90, 99, 104, 111, 115, 123, 128, 137, 142, 149, 160, 167, 168, 177, 187, 194, 205, 215, 219, 229, 235, 247, 260, 269, 271, 285, 294, 304, 313
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,8


LINKS



FORMULA

a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((nj)/2)} sign(c(i/j) + c((nij)/i) + c((nij)/j)) * (1  [j = i]) * (1  [nj = 2*i]), where c(n) = ceiling(n)  floor(n) and [ ] is the Iverson bracket.


EXAMPLE

a(9) = 2; [1,3,5], [2,3,4] (Not counted: [1,1,7], [1,2,6], [1,4,4], [2,2,5], [3,3,3]).


MATHEMATICA

Table[Sum[Sum[(1  KroneckerDelta[i, j]) (1  KroneckerDelta[2 i, n  j]) Sign[(Ceiling[i/j]  Floor[i/j]) + (Ceiling[(n  i  j)/j]  Floor[(n  i  j)/j]) + (Ceiling[(n  i  j)/i]  Floor[(n  i  j)/i])], {i, j, Floor[(n  j)/2]}], {j, Floor[n/3]}], {n, 100}]


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



