A322281 Number of permutations sigma such that |sigma(i+j)-sigma(i)| >= 4 for 1 <= i <= n - j, 1 <= j <= 3.

1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 74, 2424, 93424, 4394386, 201355480

Offset: 0

Author

Seiichi Manyama, Dec 01 2018

Keywords

• nonn
• more

Comments

2 | a(n) for n > 1.

Examples

			a(16) = 2: [4,8,12,16,3,7,11,15,2,6,10,14,1,5,9,13] and its reverse.
		

Crossrefs

Cf. A179957, A279214.

Programs

Ruby

def check(d, a, i)
  return true if i == 0
  j = 1
  d_max = [i, d - 1].min
  while (a[i] - a[i - j]).abs >= d && j < d_max
    j += 1
  end
  (a[i] - a[i - j]).abs >= d
end
def solve(d, len, a = [])
  b = []
  if a.size == len
    b << a
  else
    (1..len).each{|m|
      s = a.size
      if s == 0 || (s > 0 && !a.include?(m))
        if check(d, a + [m], s)
          b += solve(d, len, a + [m])
        end
      end
    }
  end
  b
end
def A322281(n)
  (0..n).map{|i| solve(4, i).size}
end
p A322281(18)

Extensions

a(21) from Alois P. Heinz, Dec 02 2018