cp's OEIS Frontend

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.

Showing 1-3 of 3 results.

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.

Original entry on oeis.org

1, 0, 2, 20, 752, 84008, 29145982, 30795358024, 99417240957788
Offset: 1

Views

Author

Seiichi Manyama, Mar 22 2020

Keywords

Comments

a(11) = 29262010991555584566654. - Seiichi Manyama, Apr 07 2020

Examples

			a(3) = 2;
   S--*--+   S  *--+
         |   |  |  |
   *--+--*   *  +  *
   |         |  |  |
   +--*--E   +--*  E
a(4) = 20;
   S--*--*--+   S--*--*--+   S--*--*--+
            |            |            |
   *--*--+--*   *--*--+--*   *--*  +--*
   |            |            |  |  |
   *  +--*      *  +--*--*   *  +--*
   |  |  |      |  |     |   |
   +--*  *--E   +--*     E   +--*--*--E
   S--*--*--+   S--*--*--+   S--*--*--+
            |            |            |
      *--+--*      *--+--*      *--+  *
      |            |            |  |  |
   *--+  *--*   *--+         *--+  *--*
   |     |  |   |            |
   +--*--*  E   +--*--*--E   +--*--*--E
   S--*--*--+   S--*  *--+   S--*  *--+
            |      |  |  |      |  |  |
         +--*   *--*  +  *      *--+  *
         |      |     |  |            |
   *--+--*      *  +--*  *   *--+--*--*
   |            |  |     |   |
   +--*--*--E   +--*     E   +--*--*--E
   S--*  *--+   S  *--*--+   S  *--*--+
      |  |  |   |  |     |   |  |     |
      *  +  *   *--*  +--*   *  *--+  *
      |  |  |         |      |     |  |
   *--+  *  *   *--+--*      *  +--*  *
   |     |  |   |            |  |     |
   +--*--*  E   +--*--*--E   +--*     E
   S  *--*--+   S  *--*--+   S     *--+
   |  |     |   |  |     |   |     |  |
   *  *  +--*   *  *  +--*   *--*--+  *
   |  |  |      |  |  |               |
   *  +  *      *  +  *--*   *--+--*--*
   |  |  |      |  |     |   |
   +--*  *--E   +--*     E   +--*--*--E
   S     *--+   S     *--+   S     *--+
   |     |  |   |     |  |   |     |  |
   *--*  +  *   *  *--+  *   *  *--+  *
      |  |  |   |  |     |   |  |     |
   *--+  *  *   *  +--*  *   *  +  *--*
   |     |  |   |     |  |   |  |  |
   +--*--*  E   +--*--*  E   +--*  *--E
   S     *--+   S     *--+
   |     |  |   |     |  |
   *  *--+  *   *     +  *
   |  |     |   |     |  |
   *  +     *   *  +--*  *
   |  |     |   |  |     |
   +--*     E   +--*     E

Crossrefs

Cf. A007764, A333455.

Programs

  • Python
    # Using graphillion
from graphillion import GraphSet
import graphillion.tutorial as tl
def A333464(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):
        paths = paths.including((n - 1) * (i + 1) + 1)
    return paths.len()
print([A333464(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 - 1).all?{|i| used[(n - 1) * (i + 1)] == 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)
  return 1 if n == 1
  @move = [[1, 0], [-1, 0], [0, 1], [0, -1]]
  used = Array.new(n * n, false)
  search(0, 0, n, used)
end
def A333464(n)
  (1..n).map{|i| A(i)}
end
p A333464(6)

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.

Original entry on oeis.org

1, 0, 6, 68, 6102, 1404416, 1094802826, 2524252113468
Offset: 2

Views

Author

Seiichi Manyama, Apr 05 2020

Keywords

Comments

a(11) = 407977071391342237828.

Examples

			a(2) = 1;
   +--+
   |  |
   +--+
a(4) = 6;
   +--*--*--+   +--*--*--+   +--*--*--+
   |        |   |        |   |        |
   *--+--+  *   *--+  +--*   *  +--+--*
         |  |      |  |      |  |
   *--+--+  *   *--+  +--*   *  +--+--*
   |        |   |        |   |        |
   +--*--*--+   +--*--*--+   +--*--*--+
   +--*--*--+   +--*  *--+   +--*  *--+
   |        |   |  |  |  |   |  |  |  |
   *  +--+  *   *  +--+  *   *  +  +  *
   |  |  |  |   |        |   |  |  |  |
   *  +  +  *   *  +--+  *   *  +--+  *
   |  |  |  |   |  |  |  |   |        |
   +--*  *--+   +--*  *--+   +--*--*--+

Crossrefs

Cf. A333455, A333464, A333466, A333796.

Programs

  • 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)])

A333796 Number of self-avoiding closed paths on an n X n grid which pass through all points on the diagonal connecting NW and SE corners.

Original entry on oeis.org

1, 2, 22, 716, 73346, 23374544, 23037365786, 69630317879888
Offset: 2

Views

Author

Seiichi Manyama, Apr 05 2020

Keywords

Comments

a(11) = 18267559028025887599256.

Examples

			a(2) = 1;
   +--*
   |  |
   *--+
a(3) = 2;
   +--*--*   +--*
   |     |   |  |
   *--+  *   *  +--*
      |  |   |     |
      *--+   *--*--+
a(4) = 22;
   +--*--*--*   +--*--*--*   +--*--*--*
   |        |   |        |   |        |
   *--+--*  *   *--+--*  *   *--+--*  *
         |  |         |  |         |  |
   *--*--+  *      *--+  *         +  *
   |        |      |     |         |  |
   *--*--*--+      *--*--+         *--+
   +--*--*--*   +--*--*--*   +--*--*--*
   |        |   |        |   |        |
   *--+  *--*   *--+  *--*   *--+     *
      |  |         |  |         |     |
   *--*  +--*      *  +--*      *--+  *
   |        |      |     |         |  |
   *--*--*--+      *--*--+         *--+
   +--*--*--*   +--*--*--*   +--*--*--*
   |        |   |        |   |        |
   *  +--*--*   *  +--*  *   *  +--*  *
   |  |         |  |  |  |   |  |  |  |
   *  *--+--*   *--*  +  *   *  *  +  *
   |        |         |  |   |  |  |  |
   *--*--*--+         *--+   *--*  *--+
   +--*--*      +--*--*      +--*--*
   |     |      |     |      |     |
   *--+  *--*   *--+  *      *--+  *
      |     |      |  |         |  |
      *--+  *   *--*  +--*      *  +--*
         |  |   |        |      |     |
         *--+   *--*--*--+      *--*--+
   +--*--*      +--*  *--*   +--*  *--*
   |     |      |  |  |  |   |  |  |  |
   *  +--*      *  +--*  *   *  +--*  *
   |  |         |        |   |        |
   *  *--+--*   *--*--+  *   *  *--+  *
   |        |         |  |   |  |  |  |
   *--*--*--+         *--+   *--*  *--+
   +--*  *--*   +--*         +--*
   |  |  |  |   |  |         |  |
   *  +  *  *   *  +--*--*   *  +--*--*
   |  |  |  |   |        |   |        |
   *  *--+  *   *--*--+  *   *  *--+  *
   |        |         |  |   |  |  |  |
   *--*--*--+         *--+   *--*  *--+
   +--*         +--*         +--*
   |  |         |  |         |  |
   *  +--*      *  +--*      *  +  *--*
   |     |      |     |      |  |  |  |
   *--*  +--*   *     +--*   *  *--+  *
      |     |   |        |   |        |
      *--*--+   *--*--*--+   *--*--*--+
   +--*
   |  |
   *  +
   |  |
   *  *--+--*
   |        |
   *--*--*--+

Crossrefs

Cf. A333455, A333464, A333466, A333795.

Programs

  • Python
    # Using graphillion
from graphillion import GraphSet
import graphillion.tutorial as tl
def A333796(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]
    for i in points:
        cycles = cycles.including(i)
    return cycles.len()
print([A333796(n) for n in range(2, 10)])
Showing 1-3 of 3 results.

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