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A024156 Number of integer-sided triangles with sides a,b,c, a<b<c, a+b+c=n that are obtuse. 6

%I

%S 0,0,0,0,0,0,0,0,1,0,1,0,2,1,2,2,3,2,4,3,6,3,7,4,8,6,9,7,10,8,12,10,

%T 15,11,16,13,18,15,19,17,21,19,25,21,28,22,30,25,32,28,35,31,38,33,41,

%U 35,45,38,47,42,51,46,53,50,57,52,61,55,65,58,68,63,74,67,77,71,82,74,86,77,92,82,96,87

%N Number of integer-sided triangles with sides a,b,c, a<b<c, a+b+c=n that are obtuse.

%H Jean-Fran├žois Alcover, <a href="/A024156/b024156.txt">Table of n, a(n) for n = 1..200</a>

%t r[n_] := Module[{a, b}, Reduce[a>1 && a<b && a + 2b < n && 2(a + b) > n && 2n(a + b) < 2a*b + n^2, {a, b}, Integers]];

%t a[n_] := Module[{rn = r[n]}, Which[rn === False, 0, rn[[0]] === And, 1, rn[[0]] === Or, Length[rn], True, Print["error: ", n, " ", rn]]];

%t Array[a, 84] (* _Jean-Fran├žois Alcover_, Mar 01 2019 *)

%Y Cf. A024154, A024155.

%K nonn

%O 1,13

%A _Clark Kimberling_

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Last modified August 19 18:30 EDT 2022. Contains 356229 sequences. (Running on oeis4.)