A333246
Number of self-avoiding closed paths on an n X n grid which pass through NW corner.
Original entry on oeis.org
1, 7, 97, 4111, 532269, 212372937, 263708907211, 1013068026356375, 11955420069208095719, 432101605951906251627393, 47778407166747833830058004149, 16149888968763663448192636077980753, 16675786862526496319891707194153887550751, 52568166380872328447478940416604864445574575709
Offset: 2
a(2) = 1;
+--*
| |
*--*
a(3) = 7;
+--* +--*--* +--*--* +--*
| | | | | | | |
*--* *--*--* * * * *
| | | |
*--*--* *--*
+--*--* +--*--* +--*
| | | | | |
* *--* *--* * * *--*
| | | | | |
*--* *--* *--*--*
-
# Using graphillion
from graphillion import GraphSet
import graphillion.tutorial as tl
def A333246(n):
universe = tl.grid(n - 1, n - 1)
GraphSet.set_universe(universe)
cycles = GraphSet.cycles().including(1)
return cycles.len()
print([A333246(n) for n in range(2, 10)])
A333438
Number of self-avoiding walks of any length from NW corner to its adjacent points on an n X n grid or lattice.
Original entry on oeis.org
4, 16, 196, 8224, 1064540, 424745876, 527417814424, 2026136052712752, 23910840138416191440, 864203211903812503254788, 95556814333495667660116008300, 32299777937527326896385272155961508, 33351573725052992639783414388307775101504, 105136332761744656894957880833209728891149151420
Offset: 2
a(2) = 4;
S--E S E
| |
*--*
S S--*
| |
E E--*
a(3) = 16;
S--E S E S E--* S E--*
| | | | | |
*--* *--*--* * *
| |
*--*--*
S E S E--* S E--* S E
| | | | | | | |
* * * *--* *--* * * *--*
| | | | | | | |
*--* *--* *--* *--*--*
S S--* S--* S--*--*
| | | |
E E--* E * E *
| | | |
*--* *--*--*
S--*--* S--*--* S--* S--*--*
| | | |
E--*--* E *--* E *--* E--* *
| | | | | |
*--* *--*--* *--*
-
# Using graphillion
from graphillion import GraphSet
import graphillion.tutorial as tl
def A333438(n):
universe = tl.grid(n - 1, n - 1)
GraphSet.set_universe(universe)
start, goal = 1, 2
paths = GraphSet.paths(start, goal)
return paths.len() * 2
print([A333438(n) for n in range(2, 10)])
More terms from
Ed Wynn, Jun 29 2023
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