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A279214
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.
4
1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 40, 792, 15374, 281434, 5089060, 93082532, 1743601076, 33694028152
OFFSET
0,10
COMMENTS
2 | a(n) for n > 1.
EXAMPLE
a(9) = 2: 369258147, 741852963.
PROG
(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 A279214(n)
(0..n).map{|i| solve(3, i).size}
end
p A279214(12)
CROSSREFS
Cf. A002464 (|sigma(i+1)-sigma(i)| >= 2), A127697 (|sigma(i+1)-sigma(i)| >= 3).
Sequence in context: A127186 A139747 A230133 * A264716 A264713 A012637
KEYWORD
nonn,more
AUTHOR
Seiichi Manyama, Dec 17 2016
EXTENSIONS
a(0)-a(2), a(15)-a(17) from Alois P. Heinz, Dec 01 2018
STATUS
approved