A024156 Number of integer-sided triangles with sides a,b,c, a

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

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• Jean-François Alcover, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A024154, A024155.

Programs

Mathematica

r[n_] := Module[{a, b}, Reduce[a>1 && a n && 2n(a + b) < 2a*b + n^2, {a, b}, Integers]];
a[n_] := Module[{rn = r[n]}, Which[rn === False, 0, rn[[0]] === And, 1, rn[[0]] === Or, Length[rn], True, Print["error: ", n, " ", rn]]];
Array[a, 84] (* Jean-François Alcover, Mar 01 2019 *)