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A129700 Number of n-step self-avoiding paths on octant grid starting at octant origin. 3
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, 3665682736, 9452895693, 23201772603, 59899677902 (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.
Sean A. Irvine, Java program (github)
PROG
(C)
#include <stdio.h>
#include <stdlib.h>
#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
KEYWORD
nonn,more
AUTHOR
Bill Blewett, Jun 01 2007
EXTENSIONS
a(28)-a(31) from Sean A. Irvine, Jul 03 2021
STATUS
approved

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Last modified August 26 09:55 EDT 2024. Contains 375455 sequences. (Running on oeis4.)