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 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 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

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Last modified May 19 19:45 EDT 2024. Contains 372703 sequences. (Running on oeis4.)