cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A054876 Number of pairwise incongruent triangles with integer sides and positive integer area and second longest side of length n.

This page as a plain text file.
%I A054876 #19 Jun 19 2019 17:47:46
%S A054876 0,0,0,1,2,0,0,1,0,3,0,2,4,1,4,1,4,0,0,6,1,0,0,3,10,5,0,4,6,6,0,1,1,7,
%T A054876 7,2,5,1,8,10,6,2,0,2,5,0,0,3,0,13,13,14,6,0,7,5,0,8,0,14,9,1,3,1,23,
%U A054876 3,0,13,2,9,0,6,7,9,19,4,1,12,0,14,0,8,0
%N A054876 Number of pairwise incongruent triangles with integer sides and positive integer area and second longest side of length n.
%H A054876 Amiram Eldar, <a href="/A054876/b054876.txt">Table of n, a(n) for n = 1..1000</a>
%e A054876 a(10) is 3 because there are three different integer-sided, integer-area triangles with middle side length 10, namely [9,10,17], [10,10,12], and [10,10,16].
%t A054876 okQ[x_, y_, z_] := If[x + y <=z, False, Module[{s = (x + y + z)/2}, IntegerQ[ Sqrt[s(s-x)(s-y)(s-z)]]]]; a[n_] := Module[{num = 0}, Do[Do[If[okQ[x,n,z], num++], {x,1,n}], {z,n,2n}]; num]; Array[a, 100, 0] (* _Amiram Eldar_, Jun 19 2019 *)
%Y A054876 Cf. A054875.
%K A054876 nonn
%O A054876 1,5
%A A054876 _Henry Bottomley_, May 26 2000
%E A054876 Definition corrected and offset changed by _James R. Buddenhagen_, Jan 16 2012
%E A054876 More terms from _Amiram Eldar_, Jun 19 2019