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A333795
Number of self-avoiding closed paths on an n X n grid which pass through all points on the two diagonals of the grid.
2
1, 0, 6, 68, 6102, 1404416, 1094802826, 2524252113468
OFFSET
2,3
COMMENTS
a(11) = 407977071391342237828.
EXAMPLE
a(2) = 1;
+--+
| |
+--+
a(4) = 6;
+--*--*--+ +--*--*--+ +--*--*--+
| | | | | |
*--+--+ * *--+ +--* * +--+--*
| | | | | |
*--+--+ * *--+ +--* * +--+--*
| | | | | |
+--*--*--+ +--*--*--+ +--*--*--+
+--*--*--+ +--* *--+ +--* *--+
| | | | | | | | | |
* +--+ * * +--+ * * + + *
| | | | | | | | | |
* + + * * +--+ * * +--+ *
| | | | | | | | | |
+--* *--+ +--* *--+ +--*--*--+
PROG
(Python)
# Using graphillion
from graphillion import GraphSet
import graphillion.tutorial as tl
def A333795(n):
universe = tl.grid(n - 1, n - 1)
GraphSet.set_universe(universe)
cycles = GraphSet.cycles()
points = [i + 1 for i in range(n * n) if i % n - i // n == 0 or i % n + i // n == n - 1]
for i in points:
cycles = cycles.including(i)
return cycles.len()
print([A333795(n) for n in range(2, 10)])
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Seiichi Manyama, Apr 05 2020
STATUS
approved