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, 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

Offset

1,8

Links

Table of n, a(n) for n=1..65.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} sign(c(i/j) + c((n-i-j)/i) + c((n-i-j)/j)) * (1 - [j = i]) * (1 - [n-j = 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

Cf. A343246, A343396.

Sequence in context: A179637 A054241 A277320 * A332106 A088633 A213042

Adjacent sequences: A343396 A343397 A343398 * A343400 A343401 A343402

Keyword

nonn

Author

Wesley Ivan Hurt, Apr 13 2021

Status

approved