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A338614 Number of permutations p of [n] such that |p(i) - p(i-1)| <= 3 and |p(i) - p(i-2)| <= 4.

%I A338614 #10 Nov 14 2020 20:45:12
%S A338614 1,1,2,6,24,72,124,210,394,810,1652,3168,5816,10640,19794,37292,70298,
%T A338614 131618,245146,456430,851670,1592008,2976326,5559808,10379010,
%U A338614 19374184,36175422,67562524,126185322,235650426,440038528
%N A338614 Number of permutations p of [n] such that |p(i) - p(i-1)| <= 3 and |p(i) - p(i-2)| <= 4.
%H A338614 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%p A338614 b:= proc(s, x, y) option remember; `if`(s={}, 1, add(
%p A338614       `if`((x=0 or abs(x-j)<=4) and (y=0 or abs(y-j)<=3),
%p A338614           b(s minus {j}, y, j), 0), j=s))
%p A338614     end:
%p A338614 a:= n-> b({$1..n}, 0$2):
%p A338614 seq(a(n), n=0..20);
%Y A338614 Cf. A263690, A263696, A263745, A333833, A338738.
%K A338614 nonn,more
%O A338614 0,3
%A A338614 _Alois P. Heinz_, Nov 03 2020