/* * A190318.c * Calculates the entries of Sloane's A190318 (counting obtuse isosceles triangles on an n X n grid) * * Created by Nathaniel Johnston (nathaniel@nathanieljohnston.com) * May 09, 2011 */ #include <math.h> #include <stdio.h> unsigned char pt[256][256]; FILE *file; unsigned char isObtIsosceles(unsigned short a1, unsigned short a2, unsigned short b1, unsigned short b2, unsigned short c1, unsigned short c2) { int sd1, sd2, sd3; double sqsd1, sqsd2, sqsd3; sd1 = (b1-a1)*(b1-a1) + (b2-a2)*(b2-a2); sqsd1 = sqrt(sd1); sd2 = (c1-b1)*(c1-b1) + (c2-b2)*(c2-b2); sqsd2 = sqrt(sd2); sd3 = (a1-c1)*(a1-c1) + (a2-c2)*(a2-c2); sqsd3 = sqrt(sd3); if(sqsd1 + sqsd2 > sqsd3 && sqsd2 + sqsd3 > sqsd1 && sqsd3 + sqsd1 > sqsd2 && (sd1==sd2 || sd2==sd3 || sd3==sd1) && ((b1-a1)*(c1-a1) + (b2-a2)*(c2-a2) < 0 || (c1-b1)*(a1-b1) + (c2-b2)*(a2-b2) < 0 || (a1-c1)*(b1-c1) + (a2-c2)*(b2-c2) < 0))return 1; return 0; } int main () { unsigned short a, b, c, d, a1, a2, b1, b2, maxsz, sz, sz2; unsigned long long numPts; printf("This tool will calculate the entries of Sloane's A190318 (number of obtuse isosceles triangles on an n X n grid).\nPlease enter the number of terms to compute (an integer from 1 to 255): "); scanf("%d",&maxsz); numPts = 0; file = fopen("b190318.txt","w"); fprintf(file,"1 0\n"); fclose(file); printf("1 0\n"); for(sz=2;sz<=maxsz;sz++){ numPts = 0; sz2 = sz*sz; for(a=0;a<sz2;a++){ a1 = a % sz; a2 = floor(a/sz); for(b=a+1;b<sz2;b++){ b1 = b % sz; b2 = floor(b/sz); for(c=b+1;c<sz2;c++){ if(isObtIsosceles(a1, a2, b1, b2, c % sz, floor(c/sz))){ numPts++; } } } } file = fopen("b190318.txt","a"); fprintf(file,"%d %d\n",sz,numPts); fclose(file); printf("%d %d\n",sz,numPts); } printf("Done!"); getchar(); return 0; }