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%I #22 Jul 03 2021 21:16:22
%S 1,1,2,3,8,14,36,70,177,372,942,2056,5222,11736,29878,68576,175038,
%T 408328,1044533,2468261,6326688,15107015,38791865,93432564,240296399,
%U 583001850,1501520574,3665682736,9452895693,23201772603,59899677902
%N Number of n-step self-avoiding paths on octant grid starting at octant origin.
%C 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 Guttmann-Torrie series coefficients c_n^2 for square lattice, with wedge angle Pi/4. - _N. J. A. Sloane_, Jul 06 2015
%H 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 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a129/A129700.java">Java program</a> (github)
%o (C)
%o #include <stdio.h>
%o #include <stdlib.h>
%o #define GRIDSIZE 20
%o void Recur(int level, int maxlevel, int rgBd[][GRIDSIZE], int i, int j, int rgCt[]) {
%o if (i < 0 || j < 0 || i >= GRIDSIZE || j >= GRIDSIZE || level >= maxlevel || j > i || rgBd[i][j] != 0) return;
%o rgCt[level] += 1;
%o rgBd[i][j] = 1;
%o Recur(level + 1, maxlevel, rgBd, i + 1, j, rgCt);
%o Recur(level + 1, maxlevel, rgBd, i - 1, j, rgCt);
%o Recur(level + 1, maxlevel, rgBd, i, j + 1, rgCt);
%o Recur(level + 1, maxlevel, rgBd, i, j - 1, rgCt);
%o rgBd[i][j] = 0;
%o }
%o int main(int argc, char **argv) {
%o int rgBd[GRIDSIZE][GRIDSIZE] = {0};
%o int rgCt[GRIDSIZE] = {0};
%o int maxlevel = GRIDSIZE;
%o if (argc > 1) {
%o maxlevel = atoi(argv[1]);
%o if (maxlevel < 0 || maxlevel > GRIDSIZE) {
%o printf("Bad argument");
%o return 0;
%o }
%o }
%o Recur(0, maxlevel, rgBd, 0, 0, rgCt);
%o for (int i = 0; i < maxlevel; i++) printf("%2d ", rgCt[i]);
%o return 0;
%o }
%Y Cf. A038373.
%K nonn,more
%O 1,3
%A _Bill Blewett_, Jun 01 2007
%E a(28)-a(31) from _Sean A. Irvine_, Jul 03 2021
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