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 A070093 Number of acute integer triangles with perimeter n. 21
 0, 0, 1, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 2, 4, 3, 5, 4, 5, 5, 5, 6, 6, 6, 7, 7, 9, 8, 10, 9, 10, 10, 11, 12, 12, 12, 14, 13, 16, 14, 17, 16, 17, 18, 18, 20, 20, 20, 22, 22, 24, 23, 25, 26, 26, 27, 28, 30, 30, 29, 32, 31, 35, 33, 36, 36, 38, 39, 40, 40 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,9 COMMENTS An integer triangle [A070080(k) <= A070081(k) <= A070082(k)] is acute iff A070085(k) > 0. LINKS Seiichi Manyama, Table of n, a(n) for n = 1..1000 Eric Weisstein's World of Mathematics, Acute Triangle. R. Zumkeller, Integer-sided triangles FORMULA a(n) = A005044(n) - A070101(n) - A024155(n); a(n) = A042154(n) + A070098(n). a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} (1-sign(floor((n-i-k)^2/(i^2+k^2)))) * sign(floor((i+k)/(n-i-k+1))). - Wesley Ivan Hurt, May 12 2019 EXAMPLE For n=9 there are A005044(9)=3 integer triangles: [1,4,4], [2,3,4] and [3,3,3]; two of them are acute, as 2^2+3^2<16=4^2, therefore a(9)=2. MATHEMATICA Table[Sum[Sum[(1 - Sign[Floor[(n - i - k)^2/(i^2 + k^2)]]) Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}] (* Wesley Ivan Hurt, May 12 2019 *) CROSSREFS Cf. A070094, A070095, A070118. Cf. A005044, A024155, A070101. Sequence in context: A293223 A361514 A029348 * A174931 A058744 A366297 Adjacent sequences: A070090 A070091 A070092 * A070094 A070095 A070096 KEYWORD nonn AUTHOR Reinhard Zumkeller, May 05 2002 STATUS approved

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Last modified April 22 17:45 EDT 2024. Contains 371906 sequences. (Running on oeis4.)