A292793 1/4 of the number of self-avoiding paths that are made of alternated vertical and horizontal n consecutive steps. (start point is different from end point.)

1, 2, 4, 8, 16, 29, 54, 98, 176, 318, 572, 1026, 1826, 3255, 5794, 10233, 18172, 32012, 56488, 99469, 175034, 307479, 540068, 947235, 1659907, 2908958, 5095019, 8917677, 15598100, 27281252, 47718310, 83298748, 145405769, 253641303, 442352671, 770769569, 1343166519, 2339093953

Offset

2,2

Links

Table of n, a(n) for n=2..39.

Example

a(2) = 1;
   E
   |
   *
   |
S--*
a(3) = 2;
   *--*--*--E     E--*--*--*
   |                       |
   *                       *
   |                       |
S--*                    S--*
a(4) = 4;
            E                                      E
            |                                      |
            *                                      *
            |                                      |
            *                                      *
            |                                      |
            *                                      *
            |                                      |
   *--*--*--*        *--*--*--*     *--*--*--*     *--*--*--*
   |                 |        |     |        |              |
   *                 *        *     *        *              *
   |                 |        |     |        |              |
S--*              S--*        *     *     S--*           S--*
                              |     |
                              E     E

Prog

(Ruby)
def A292793(n)
  ary = [1]
  b_ary = [[[0, 0], [1, 0], [1, 1], [1, 2]]]
  s = 4
  (3..n).each{|i|
    s += i
    f_ary, b_ary = b_ary, []
    if i % 2 == 1
      f_ary.each{|a|
        b = a.clone
        x, y = *b[-1]
        b += (1..i).map{|j| [x + j, y]}
        b_ary << b if b.uniq.size == s
        c = a.clone
        x, y = *c[-1]
        c += (1..i).map{|j| [x - j, y]}
        b_ary << c if c.uniq.size == s
      }
    else
      f_ary.each{|a|
        b = a.clone
        x, y = *b[-1]
        b += (1..i).map{|j| [x, y + j]}
        b_ary << b if b.uniq.size == s
        c = a.clone
        x, y = *c[-1]
        c += (1..i).map{|j| [x, y - j]}
        b_ary << c if c.uniq.size == s
      }
    end
    ary << b_ary.size
  }
  ary
end
p A292793(16)

Crossrefs

Cf. A101856.

Sequence in context: A085583 A160786 A054154 * A332835 A018469 A098904

Adjacent sequences: A292790 A292791 A292792 * A292794 A292795 A292796

Keyword

nonn

Author

Seiichi Manyama, Sep 23 2017

Extensions

a(25)-a(39) from Bert Dobbelaere, Sep 14 2019

Status

approved