A242521[n_] := Count[Map[lpf, Map[j1f, Permutations[Range[2, n]]]], 0]/2;
j1f[x_] := Join[{1}, x, {1}];
lpf[x_] := Length[Select[Abs[Differences[x]], ! MemberQ[t, #] &]];
t = Flatten[Table[b^k, {k, 2, 5}, {b, 2, 5}]];
(* OR, a less simple, but more efficient implementation. *)
A242521[n_, perm_, remain_] := Module[{opt, lr, i, new},
If[remain == {},
If[MemberQ[t, Abs[First[perm] - Last[perm]]], ct++];
Return[ct],
opt = remain; lr = Length[remain];
For[i = 1, i <= lr, i++,
new = First[opt]; opt = Rest[opt];
If[! MemberQ[t, Abs[Last[perm] - new]], Continue[]];
Complement[Range[2, n], perm, {new}]];
];
Return[ct];
];
];
t = Flatten[Table[b^k, {k, 2, 5}, {b, 2, 5}]];
