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A328648 Number of permutations p of [n] such that |p(i) - p(i-1)| is in {2,7} for all i from 2 to n.

%I A328648 #17 Oct 23 2021 14:24:57
%S A328648 1,1,0,0,0,0,0,0,2,18,12,0,12,62,76,32,44,162,600,714,386,550,2514,
%T A328648 5320,4140,3336,8626,24722,33428,27110,34812,96210,200322,220360,
%U A328648 213368,376178,894780,1400578,1473944,1810538,3653304,7170370,9467970
%N A328648 Number of permutations p of [n] such that |p(i) - p(i-1)| is in {2,7} for all i from 2 to n.
%C A328648 For n>1, a(n)/2 is the number of Hamiltonian paths on the graph with vertex set {1,...,n} where i is adjacent to j iff |i-j| is in {2,7}.
%e A328648 a(8) = 2: 24681357, 75318642.
%e A328648 a(9) = 18: 135792468, 186429753, 246813579, 297531864, 318642975, 357924681, 429753186, 468135792, 531864297, 579246813, 642975318, 681357924, 753186429, 792468135, 813579246, 864297531, 924681357, 975318642.
%e A328648 a(10) = 12: 135792468(10), 13(10)8642975, 186429753(10), 18(10)3579246, 579246813(10), 5792468(10)31, 642975318(10), 6429753(10)81, (10)318642975, (10)357924681, (10)813579246, (10)864297531.
%p A328648 b:= proc(s, l) option remember; `if`(s={}, 1, add(`if`(l=0
%p A328648       or abs(l-j) in {2, 7}, b(s minus {j}, j), 0), j=s))
%p A328648     end:
%p A328648 a:= n-> b({$1..n}, 0):
%p A328648 seq(a(n), n=0..20);
%t A328648 b[s_, l_] := b[s, l] = If[s == {}, 1, Sum[If[l == 0 || MemberQ[{2, 7}, Abs[l - j]], b[s ~Complement~ {j}, j], 0], {j, s}]];
%t A328648 a[n_] := b[Range[n], 0];
%t A328648 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Oct 23 2021, after _Alois P. Heinz_ *)
%Y A328648 Cf. A174703, A174708, A302118, A307269.
%K A328648 nonn
%O A328648 0,9
%A A328648 _Alois P. Heinz_, Oct 23 2019