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%I #17 Dec 02 2018 12:00:52
%S 1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,74,2424,93424,4394386,201355480
%N Number of permutations sigma such that |sigma(i+j)-sigma(i)| >= 4 for 1 <= i <= n - j, 1 <= j <= 3.
%C 2 | a(n) for n > 1.
%e a(16) = 2: [4,8,12,16,3,7,11,15,2,6,10,14,1,5,9,13] and its reverse.
%o (Ruby)
%o def check(d, a, i)
%o return true if i == 0
%o j = 1
%o d_max = [i, d - 1].min
%o while (a[i] - a[i - j]).abs >= d && j < d_max
%o j += 1
%o end
%o (a[i] - a[i - j]).abs >= d
%o end
%o def solve(d, len, a = [])
%o b = []
%o if a.size == len
%o b << a
%o else
%o (1..len).each{|m|
%o s = a.size
%o if s == 0 || (s > 0 && !a.include?(m))
%o if check(d, a + [m], s)
%o b += solve(d, len, a + [m])
%o end
%o end
%o }
%o end
%o b
%o end
%o def A322281(n)
%o (0..n).map{|i| solve(4, i).size}
%o end
%o p A322281(18)
%Y Cf. A179957, A279214.
%K nonn,more
%O 0,17
%A _Seiichi Manyama_, Dec 01 2018
%E a(21) from _Alois P. Heinz_, Dec 02 2018
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