a(n) = (n*3^(n+1)+((5*3^(n+1)+(-1)^(n))/4))/4.

Terms

a(0) =1a(1) =5a(2) =22a(3) =86a(4) =319a(5) =1139a(6) =3964a(7) =13532a(8) =45517a(9) =151313a(10) =498226a(11) =1627538a(12) =5281195a(13) =17039327a(14) =54705208a(15) =174877304a(16) =556916953a(17) =1767605981a(18) =5593383310a(19) =17651846030a(20) =55570626391a(21) =174557144075a(22) =547207226932