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 A129700 Number of n-step self-avoiding paths on octant grid starting at octant origin. 0
 1, 1, 2, 3, 8, 14, 36, 70, 177, 372, 942, 2056, 5222, 11736, 29878, 68576, 175038, 408328, 1044533, 2468261, 6326688, 15107015, 38791865, 93432564, 240296399, 583001850, 1501520574 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS 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. Guttmann-Torrie series coefficients c_n^2 for square lattice, with wedge angle Pi/4. - N. J. A. Sloane, Jul 06 2015 LINKS A. J. Guttmann and G. M. Torrie, Critical behavior at an edge for the SAW and Ising model, J. Phys. A 17 (1984), 3539-3552. PROG (C) #include #include #define GRIDSIZE 20 void Recur(int level, int maxlevel, int rgBd[][GRIDSIZE], int i, int j, int rgCt[]) {   if (i < 0 || j < 0 || i >= GRIDSIZE || j >= GRIDSIZE || level >= maxlevel || j > i || rgBd[i][j] != 0) return;   rgCt[level] += 1;   rgBd[i][j] = 1;   Recur(level + 1, maxlevel, rgBd, i + 1, j, rgCt);   Recur(level + 1, maxlevel, rgBd, i - 1, j, rgCt);   Recur(level + 1, maxlevel, rgBd, i, j + 1, rgCt);   Recur(level + 1, maxlevel, rgBd, i, j - 1, rgCt);   rgBd[i][j] = 0; } int main(int argc, char **argv) {   int rgBd[GRIDSIZE][GRIDSIZE] = {0};   int rgCt[GRIDSIZE] = {0};   int maxlevel = GRIDSIZE;   if (argc > 1) {     maxlevel = atoi(argv[1]);     if (maxlevel < 0 || maxlevel > GRIDSIZE) {       printf("Bad argument");       return 0;     }   }   Recur(0, maxlevel, rgBd, 0, 0, rgCt);   for (int i = 0; i < maxlevel; i++) printf("%2d ", rgCt[i]);   return 0; } CROSSREFS Cf. A038373. Sequence in context: A298349 A298343 A201361 * A197466 A049344 A080877 Adjacent sequences:  A129697 A129698 A129699 * A129701 A129702 A129703 KEYWORD nonn AUTHOR Bill Blewett, Jun 01 2007 STATUS approved

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Last modified February 29 07:39 EST 2020. Contains 332355 sequences. (Running on oeis4.)