a(n) = (1/2)*s(n+3), where s = A025244.

Terms

a(0) =1a(1) =2a(2) =5a(3) =11a(4) =26a(5) =65a(6) =163a(7) =416a(8) =1081a(9) =2837a(10) =7516a(11) =20089a(12) =54077a(13) =146478a(14) =398997a(15) =1092215a(16) =3003014a(17) =8289569a(18) =22964919a(19) =63828252a(20) =177931665a(21) =497367721a(22) =1393768952a(23) =3914793457a(24) =11019379609a(25) =31079140922a(26) =87818240869a(27) =248571086403a(28) =704722488690