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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. 1
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 (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((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
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Apr 13 2021
STATUS
approved

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Last modified June 20 08:48 EDT 2024. Contains 373515 sequences. (Running on oeis4.)