A343396 Number of partitions of n into 3 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, 1, 3, 3, 4, 7, 8, 9, 12, 13, 16, 20, 21, 25, 27, 28, 34, 41, 42, 43, 49, 54, 57, 65, 65, 73, 79, 82, 89, 94, 97, 106, 114, 118, 123, 133, 135, 147, 153, 155, 168, 181, 182, 188, 195, 207, 214, 229, 233, 240, 249, 258, 272, 287, 286, 299, 312, 316, 330, 339

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)), where c(n) = ceiling(n) - floor(n).

Example

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

Mathematica

Table[Sum[Sum[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.

Sequence in context: A058674 A349252 A152651 * A091973 A328798 A327726

Adjacent sequences: A343393 A343394 A343395 * A343397 A343398 A343399

Keyword

nonn

Author

Wesley Ivan Hurt, Apr 13 2021

Status

approved