The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A070101 Number of obtuse integer triangles with perimeter n. 17
 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 2, 3, 2, 3, 3, 5, 3, 7, 4, 8, 5, 9, 7, 10, 8, 11, 9, 14, 11, 16, 12, 18, 14, 19, 17, 21, 18, 23, 21, 27, 22, 30, 24, 32, 27, 34, 30, 37, 33, 40, 35, 44, 37, 47, 40, 50, 44, 53, 49, 56, 52, 60, 55, 64, 57, 68 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,11 COMMENTS An integer triangle [A070080(k) <= A070081(k) <= A070082(k)] is obtuse iff A070085(k) < 0. LINKS Seiichi Manyama, Table of n, a(n) for n = 1..1000 Eric Weisstein's World of Mathematics, Obtuse Triangle. R. Zumkeller, Integer-sided triangles FORMULA a(n) = A005044(n) - A070093(n) - A024155(n). a(n) = A024156(n) + A070106(n). a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} (1-sign(floor((i^2 + k^2)/(n-i-k)^2))) * sign(floor((i+k)/(n-i-k+1))). - Wesley Ivan Hurt, May 12 2019 EXAMPLE For n=14 there are A005044(14)=4 integer triangles: [2,6,6], [3,5,6], [4,4,6] and [4,5,5]; two of them are obtuse, as 3^2+5^2<36=6^2 and 4^2+4^2<36=6^2, therefore a(14)=2. MATHEMATICA Table[Sum[Sum[(1 - Sign[Floor[(i^2 + k^2)/(n - i - 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. A070102, A070103, A070127. Cf. A005044, A024155, A070093. Sequence in context: A288311 A244366 A262676 * A022830 A035663 A117192 Adjacent sequences:  A070098 A070099 A070100 * A070102 A070103 A070104 KEYWORD nonn AUTHOR Reinhard Zumkeller, May 05 2002 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 25 07:29 EDT 2020. Contains 334584 sequences. (Running on oeis4.)