Number of permutations p of [n] such that | |p(i) - p(i-1)| - |p(i+1) - p(i)| | <= 1.

Terms

a(0) =1a(1) =1a(2) =2a(3) =6a(4) =18a(5) =38a(6) =76a(7) =162a(8) =330a(9) =650a(10) =1272a(11) =2586a(12) =5262a(13) =10506a(14) =20856a(15) =41928a(16) =83684a(17) =165800a(18) =329310a(19) =653614a(20) =1303388a(21) =2584660a(22) =5139580a(23) =10210912a(24) =20288128a(25) =40224174a(26) =79824572a(27) =158316222a(28) =314272812