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A129700
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Number of n-step self-avoiding paths on octant grid starting at octant origin.
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0
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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
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OFFSET
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1,3
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COMMENTS
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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. It's 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.
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LINKS
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Table of n, a(n) for n=1..27.
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PROG
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// C++ code #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; }
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CROSSREFS
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Cf. A038373.
Sequence in context: A173149 A128305 A201361 * A197466 A049344 A080877
Adjacent sequences: A129697 A129698 A129699 * A129701 A129702 A129703
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KEYWORD
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nonn
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AUTHOR
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Bill Blewett, Jun 01 2007
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STATUS
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approved
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