login
A333674
Number of self-avoiding closed paths on a (2*n+1) X (2*n+1) grid which pass through the center of (2*n+1) X (2*n+1) grid.
2
12, 6820, 377147460, 1839271833471556, 784401089017645862031632, 29302016786723196117858460309272916
OFFSET
1,1
COMMENTS
a(n) is a multiple of 4.
EXAMPLE
a(1) = 12;
*--*--* *--*--* *--*--* *--* *--* *--*
| | | | | | | | | | | |
*--+ * * +--* *--+--* * +--* * + *--+
| | | | | | | |
*--* *--* *--*--* *--*
*--* *--* *--*
| | | | | |
+ * *--+ * +--* +--* *--+--* *--+
| | | | | | | | | |
*--* *--*--* *--* *--*--* *--*
PROG
(Python)
# Using graphillion
from graphillion import GraphSet
import graphillion.tutorial as tl
def A333674(n):
universe = tl.grid(2 * n, 2 * n)
GraphSet.set_universe(universe)
cycles = GraphSet.cycles().including(2 * n * n + 2 * n + 1)
return cycles.len()
print([A333674(n) for n in range(1, 6)])
CROSSREFS
Cf. A121787.
Sequence in context: A208865 A012607 A167072 * A308130 A107251 A201493
KEYWORD
nonn,more,hard
AUTHOR
Seiichi Manyama, Apr 01 2020
EXTENSIONS
a(6) from Lucas A. Brown, Mar 19 2024
STATUS
approved