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

Terms

a(0) =1a(1) =1a(2) =2a(3) =2a(4) =8a(5) =12a(6) =32a(7) =40a(8) =88a(9) =118a(10) =244a(11) =338a(12) =642a(13) =912a(14) =1650a(15) =2402a(16) =4182a(17) =6200a(18) =10492a(19) =15786a(20) =26166a(21) =39814a(22) =64994a(23) =99738a(24) =161020a(25) =248670a(26) =398248a(27) =617912a(28) =983890a(29) =1531796