Number of permutations of [n] realized by the shift on 3 letters.

Terms

a(0) =2a(1) =6a(2) =24a(3) =114a(4) =528a(5) =2334a(6) =9528a(7) =36834a(8) =135918a(9) =484206a(10) =1678152a(11) =5694786a(12) =19007808a(13) =62625054a(14) =204215340a(15) =660445914a(16) =2121665016a(17) =6778399914a(18) =21557206332a(19) =68294432778a(20) =215651021484a(21) =679023425238