Number of key permutations of length n: permutations {a_i} with |a_i - a_{i-1}| = 1 or 2.

Terms

a(0) =1a(1) =1a(2) =2a(3) =6a(4) =12a(5) =20a(6) =34a(7) =56a(8) =88a(9) =136a(10) =208a(11) =314a(12) =470a(13) =700a(14) =1038a(15) =1534a(16) =2262a(17) =3330a(18) =4896a(19) =7192a(20) =10558a(21) =15492a(22) =22724a(23) =33324a(24) =48860a(25) =71630a(26) =105002a(27) =153912a(28) =225594a(29) =330650