A051519 - OEIS

%I #21 Jul 02 2022 01:50:58

%S 12,32,48,36,64,98,160,84,128,168,144,108,416,196,192,216,288,256,780,

%T 336,294,612,396,378,1026,392,448,420,512,324,600,792,800,432,484,540,

%U 1000,810,676,576,1760,2842,1250,648,726,924,980,2484,1134,864,1210,784

%N Exactly n integer-sided triangles of perimeter a(n) have integer area.

%H Randall L Rathbun, <a href="/A051519/b051519.txt">Table of n, a(n) for n = 1..229</a>

%o (C)

%o #include <stdio.h> /* printf() */ #include <math.h> /* sqrt() round() */

%o unsigned int is_triangle(int a, int b, int c) { double s,A,B; s = (a+b+c)/2.0; A = s*(s-a)*(s-b)*(s-c); B = floor(sqrt(A)+0.1); if ( B*B == A && A > 0.0 ) return 1; else return 0; }

%o int main() { int set; int a,b,c,p; for (p=1; p<15001; p++) { printf("%d ",p); set = 0; for (a=1; a<p; a++) { for (b=a; b<p; b++) { c = p-a-b; if (c >=b && c < a+b && b < a+c && a < b+c ) { if (is_triangle(a,b,c)) { set += 1; printf("[%d %d %d] ",a,b,c); } } } } printf(" "); printf("perimeter %d = %d ",p,set); } return 0; } /* _Randall L Rathbun_, Jan 26 2007 */

%K nonn

%O 1,1

%A _David W. Wilson_

%E More terms from _Randall L Rathbun_, Jan 26 2007