This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A333464 #32 Apr 07 2020 10:38:43
%S A333464 1,0,2,20,752,84008,29145982,30795358024,99417240957788
%N A333464 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 NE and SW corners.
%C A333464 a(11) = 29262010991555584566654. - _Seiichi Manyama_, Apr 07 2020
%e A333464 a(3) = 2;
%e A333464 S--*--+ S *--+
%e A333464 | | | |
%e A333464 *--+--* * + *
%e A333464 | | | |
%e A333464 +--*--E +--* E
%e A333464 a(4) = 20;
%e A333464 S--*--*--+ S--*--*--+ S--*--*--+
%e A333464 | | |
%e A333464 *--*--+--* *--*--+--* *--* +--*
%e A333464 | | | | |
%e A333464 * +--* * +--*--* * +--*
%e A333464 | | | | | | |
%e A333464 +--* *--E +--* E +--*--*--E
%e A333464 S--*--*--+ S--*--*--+ S--*--*--+
%e A333464 | | |
%e A333464 *--+--* *--+--* *--+ *
%e A333464 | | | | |
%e A333464 *--+ *--* *--+ *--+ *--*
%e A333464 | | | | |
%e A333464 +--*--* E +--*--*--E +--*--*--E
%e A333464 S--*--*--+ S--* *--+ S--* *--+
%e A333464 | | | | | | |
%e A333464 +--* *--* + * *--+ *
%e A333464 | | | | |
%e A333464 *--+--* * +--* * *--+--*--*
%e A333464 | | | | |
%e A333464 +--*--*--E +--* E +--*--*--E
%e A333464 S--* *--+ S *--*--+ S *--*--+
%e A333464 | | | | | | | | |
%e A333464 * + * *--* +--* * *--+ *
%e A333464 | | | | | | |
%e A333464 *--+ * * *--+--* * +--* *
%e A333464 | | | | | | |
%e A333464 +--*--* E +--*--*--E +--* E
%e A333464 S *--*--+ S *--*--+ S *--+
%e A333464 | | | | | | | | |
%e A333464 * * +--* * * +--* *--*--+ *
%e A333464 | | | | | | |
%e A333464 * + * * + *--* *--+--*--*
%e A333464 | | | | | | |
%e A333464 +--* *--E +--* E +--*--*--E
%e A333464 S *--+ S *--+ S *--+
%e A333464 | | | | | | | | |
%e A333464 *--* + * * *--+ * * *--+ *
%e A333464 | | | | | | | | |
%e A333464 *--+ * * * +--* * * + *--*
%e A333464 | | | | | | | | |
%e A333464 +--*--* E +--*--* E +--* *--E
%e A333464 S *--+ S *--+
%e A333464 | | | | | |
%e A333464 * *--+ * * + *
%e A333464 | | | | | |
%e A333464 * + * * +--* *
%e A333464 | | | | | |
%e A333464 +--* E +--* E
%o A333464 (Python)
%o A333464 # Using graphillion
%o A333464 from graphillion import GraphSet
%o A333464 import graphillion.tutorial as tl
%o A333464 def A333464(n):
%o A333464 if n == 1: return 1
%o A333464 universe = tl.grid(n - 1, n - 1)
%o A333464 GraphSet.set_universe(universe)
%o A333464 start, goal = 1, n * n
%o A333464 paths = GraphSet.paths(start, goal)
%o A333464 for i in range(n):
%o A333464 paths = paths.including((n - 1) * (i + 1) + 1)
%o A333464 return paths.len()
%o A333464 print([A333464(n) for n in range(1, 10)])
%o A333464 (Ruby)
%o A333464 def search(x, y, n, used)
%o A333464 return 0 if x < 0 || n <= x || y < 0 || n <= y || used[x + y * n]
%o A333464 return 1 if x == n - 1 && y == n - 1 && (0..n - 1).all?{|i| used[(n - 1) * (i + 1)] == true}
%o A333464 cnt = 0
%o A333464 used[x + y * n] = true
%o A333464 @move.each{|mo|
%o A333464 cnt += search(x + mo[0], y + mo[1], n, used)
%o A333464 }
%o A333464 used[x + y * n] = false
%o A333464 cnt
%o A333464 end
%o A333464 def A(n)
%o A333464 return 1 if n == 1
%o A333464 @move = [[1, 0], [-1, 0], [0, 1], [0, -1]]
%o A333464 used = Array.new(n * n, false)
%o A333464 search(0, 0, n, used)
%o A333464 end
%o A333464 def A333464(n)
%o A333464 (1..n).map{|i| A(i)}
%o A333464 end
%o A333464 p A333464(6)
%Y A333464 Cf. A007764, A333455.
%K A333464 nonn,more
%O A333464 1,3
%A A333464 _Seiichi Manyama_, Mar 22 2020