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Number of integer triangles with perimeter n which are acute and isosceles.
8

%I #23 Sep 08 2022 08:45:05

%S 0,0,1,0,1,1,1,1,2,2,2,2,3,2,3,3,4,3,4,4,4,4,5,4,5,5,6,5,6,6,6,6,7,7,

%T 7,7,8,7,8,8,8,8,9,9,9,9,10,9,10,10,11,10,11,11,11,11,12,12,12,12,13,

%U 12,13,13,13,13,14,14,14,14,15,14,15,15,16,15

%N Number of integer triangles with perimeter n which are acute and isosceles.

%C Equivalently, the number of obtuse isosceles integer triangles with base n. - _Charlie Marion_, Jun 18 2019

%H Marius A. Burtea, <a href="/A070098/b070098.txt">Table of n, a(n) for n = 1..10000</a>

%H Reinhard Zumkeller, <a href="/A070080/a070080.txt">Integer-sided triangles</a>

%F a(n) = A070093(n)-A024154(n); a(n) = A059169(n)-A070106(n).

%F a(n) = floor(n/2) - floor(n/(2 + sqrt(2))) - ((n + 1) mod 2). - _David Pasino_, Jun 27 2016

%F a(n) = A004526(n-1) - A183138(n). - _R. J. Mathar_, May 22 2019

%e For n=9 there are A005044(9)=3 integer triangles: [1,4,4], [2,3,4] and [3,3,3]; both isosceles are also acute.

%o (Magma) [Floor(k/2)-Floor(k/(2 + Sqrt(2)))-((k + 1) mod 2): k in [1..76]]; // _Marius A. Burtea_, Jun 21 2019

%Y Cf. A070080, A070081, A070082, A059169, A070099, A070100, A070124.

%K nonn

%O 1,9

%A _Reinhard Zumkeller_, May 05 2002