Walks of length n on the x-axis using steps {1,0,-1} and visiting no point more than twice.

Terms

a(0) =1a(1) =4a(2) =12a(3) =30a(4) =66a(5) =148a(6) =316a(7) =682a(8) =1438a(9) =3052a(10) =6428a(11) =13574a(12) =28594a(13) =60284a(14) =127004a(15) =267634a(16) =563870a(17) =1188084a(18) =2503180a(19) =5274062a(20) =11112002a(21) =23412164a(22) =49327516a(23) =103929178a(24) =218970366a(25) =461352988a(26) =972033500a(27) =2047996278a(28) =4314962930a(29) =9091278956