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%I #79 Dec 02 2018 02:57:08
%S 1,1,0,0,0,0,0,0,0,2,40,792,15374,281434,5089060,93082532,1743601076,
%T 33694028152
%N Number of permutations sigma such that |sigma(i+1)-sigma(i)| >= 3 for 1 <= i <= n - 1 and |sigma(i+2)-sigma(i)| >= 3 for 1 <= i <= n - 2.
%C 2 | a(n) for n > 1.
%e a(9) = 2: 369258147, 741852963.
%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 A279214(n)
%o (0..n).map{|i| solve(3, i).size}
%o end
%o p A279214(12)
%Y Cf. A002464 (|sigma(i+1)-sigma(i)| >= 2), A127697 (|sigma(i+1)-sigma(i)| >= 3).
%K nonn,more
%O 0,10
%A _Seiichi Manyama_, Dec 17 2016
%E a(0)-a(2), a(15)-a(17) from _Alois P. Heinz_, Dec 01 2018
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