cp's OEIS Frontend

A129700 Number of n-step self-avoiding paths on octant grid starting at octant origin.

%I A129700 #22 Jul 03 2021 21:16:22
%S A129700 1,1,2,3,8,14,36,70,177,372,942,2056,5222,11736,29878,68576,175038,
%T A129700 408328,1044533,2468261,6326688,15107015,38791865,93432564,240296399,
%U A129700 583001850,1501520574,3665682736,9452895693,23201772603,59899677902
%N A129700 Number of n-step self-avoiding paths on octant grid starting at octant origin.
%C A129700 Similar to A038373 but with octant grid instead of quadrant. An octant grid is either half of a quadrant grid when divided on the diagonal and including the diagonal grid squares. Its shape is that of a right triangle with a stair step edge on the hypotenuse. Coordinates of squares satisfy x>=0 and y>=0 and x>=y.
%C A129700 Guttmann-Torrie series coefficients c_n^2 for square lattice, with wedge angle Pi/4. - _N. J. A. Sloane_, Jul 06 2015
%H A129700 A. J. Guttmann and G. M. Torrie, <a href="https://doi.org/10.1088/0305-4470/17/18/023">Critical behavior at an edge for the SAW and Ising model</a>, J. Phys. A 17 (1984), 3539-3552.
%H A129700 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a129/A129700.java">Java program</a> (github)
%o A129700 (C)
%o A129700 #include <stdio.h>
%o A129700 #include <stdlib.h>
%o A129700 #define GRIDSIZE 20
%o A129700 void Recur(int level, int maxlevel, int rgBd[][GRIDSIZE], int i, int j, int rgCt[]) {
%o A129700   if (i < 0 || j < 0 || i >= GRIDSIZE || j >= GRIDSIZE || level >= maxlevel || j > i || rgBd[i][j] != 0) return;
%o A129700   rgCt[level] += 1;
%o A129700   rgBd[i][j] = 1;
%o A129700   Recur(level + 1, maxlevel, rgBd, i + 1, j, rgCt);
%o A129700   Recur(level + 1, maxlevel, rgBd, i - 1, j, rgCt);
%o A129700   Recur(level + 1, maxlevel, rgBd, i, j + 1, rgCt);
%o A129700   Recur(level + 1, maxlevel, rgBd, i, j - 1, rgCt);
%o A129700   rgBd[i][j] = 0;
%o A129700 }
%o A129700 int main(int argc, char **argv) {
%o A129700   int rgBd[GRIDSIZE][GRIDSIZE] = {0};
%o A129700   int rgCt[GRIDSIZE] = {0};
%o A129700   int maxlevel = GRIDSIZE;
%o A129700   if (argc > 1) {
%o A129700     maxlevel = atoi(argv[1]);
%o A129700     if (maxlevel < 0 || maxlevel > GRIDSIZE) {
%o A129700       printf("Bad argument");
%o A129700       return 0;
%o A129700     }
%o A129700   }
%o A129700   Recur(0, maxlevel, rgBd, 0, 0, rgCt);
%o A129700   for (int i = 0; i < maxlevel; i++) printf("%2d ", rgCt[i]);
%o A129700   return 0;
%o A129700 }
%Y A129700 Cf. A038373.
%K A129700 nonn,more
%O A129700 1,3
%A A129700 _Bill Blewett_, Jun 01 2007
%E A129700 a(28)-a(31) from _Sean A. Irvine_, Jul 03 2021