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) =4a(4) =16a(5) =20a(6) =32a(7) =56a(8) =148a(9) =136a(10) =186a(11) =328a(12) =894a(13) =868a(14) =1196a(15) =1896a(16) =5210a(17) =4936a(18) =6716a(19) =11264a(20) =30046a(21) =28168a(22) =38892a(23) =63272a(24) =169900a(25) =161848a(26) =218944a(27) =367616a(28) =966010a(29) =909192