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A333455 Number of self-avoiding walks from NW to SE corners on an n X n grid which pass through all points on the diagonal connecting NW and SE corners. 4
1, 2, 10, 124, 4620, 536360, 189313340, 201653395768, 651683788574786 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
a(11) = 191874208353355680763886. - Seiichi Manyama, Apr 07 2020
LINKS
EXAMPLE
a(2) = 2;
S--* S
| |
E *--E
a(3) = 10;
S--*--* S--*--* S--*
| | |
+--* *--+--* +--*
| | |
*--E *--*--E E
S--* S--* S *--*
| | | | |
+ *--+ * + *
| | | | |
*--E *--*--E *--* E
S *--* S S
| | | | |
*--+ * * +--* *--+--*
| | | | |
E *--* E E
S
|
*--+
|
*--E
a(4) = 124;
S--*--*--* S--*--*--* S--*--*--*
| | |
*--+--* * *--+--* * *--+ *--*
| | | | | | | | |
*--* +--* * +--* * *--+
| | |
*--*--E *--*--*--E *--*--*--E
... and so on.
PROG
(Python)
# Using graphillion
from graphillion import GraphSet
import graphillion.tutorial as tl
def A333455(n):
if n == 1: return 1
universe = tl.grid(n - 1, n - 1)
GraphSet.set_universe(universe)
start, goal = 1, n * n
paths = GraphSet.paths(start, goal)
for i in range(n - 1):
paths = paths.including((n + 1) * i + 1)
return paths.len()
print([A333455(n) for n in range(1, 10)])
(Ruby)
def search(x, y, n, used)
return 0 if x < 0 || n <= x || y < 0 || n <= y || used[x + y * n]
return 1 if x == n - 1 && y == n - 1 && (0..n - 2).all?{|i| used[(n + 1) * i] == true}
cnt = 0
used[x + y * n] = true
@move.each{|mo|
cnt += search(x + mo[0], y + mo[1], n, used)
}
used[x + y * n] = false
cnt
end
def A(n)
@move = [[1, 0], [-1, 0], [0, 1], [0, -1]]
used = Array.new(n * n, false)
search(0, 0, n, used)
end
def A333455(n)
(1..n).map{|i| A(i)}
end
p A333455(6)
CROSSREFS
Sequence in context: A348876 A092645 A346372 * A334555 A202950 A144835
KEYWORD
nonn,more
AUTHOR
Seiichi Manyama, Mar 22 2020
STATUS
approved

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Last modified March 28 16:12 EDT 2024. Contains 371254 sequences. (Running on oeis4.)