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A302118 Number of permutations p of [n] such that |p(i) - p(i-1)| is in {1,3} for all i from 2 to n.

%I A302118 #23 Nov 04 2019 10:37:57
%S A302118 1,1,2,2,8,12,32,40,88,118,244,338,642,912,1650,2402,4182,6200,10492,
%T A302118 15786,26166,39814,64994,99738,161020,248670,398248,617912,983890,
%U A302118 1531796,2428988,3790980,5993746,9371174,14785512,23146268,36465816,57137316,89924384
%N A302118 Number of permutations p of [n] such that |p(i) - p(i-1)| is in {1,3} for all i from 2 to n.
%H A302118 Alois P. Heinz, <a href="/A302118/b302118.txt">Table of n, a(n) for n = 0..5100</a>
%H A302118 <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-2,-1,-1,-3,1,1,3,1,1,0,-2,0,-1)
%F A302118 G.f.: (x^16 -3*x^15 -2*x^14 +3*x^12 +6*x^11 +2*x^10 -6*x^9 -10*x^8 -6*x^7 +6*x^6 +4*x^5 +3*x^4 -x^3 -2*x^2+1) / ((x-1) *(x+1) *(x^5+x^3+x-1) *(x^4+x^2-1)^2).
%F A302118 a(n) = 2 * A302119(n) for n > 1.
%F A302118 Limit_{n->infinity} a(n)/a(n+1) = A293560 = 1/A293506 = 0.63688291680184484849...
%e A302118 a(3) = 2: 123, 321.
%e A302118 a(4) = 8: 1234, 1432, 2143, 2341, 3214, 3412, 4123, 4321.
%e A302118 a(5) = 12: 12345, 12543, 14325, 14523, 32145, 32541, 34125, 34521, 52143, 52341, 54123, 54321.
%Y A302118 Cf. A003274, A174700, A293506, A293560, A302119, A307269, A328648.
%K A302118 nonn,easy
%O A302118 0,3
%A A302118 _Alois P. Heinz_, Apr 01 2018