a(n)=4a(n-1)+C(n+3,3),n>0, a(0)=1.

Terms

a(0) =1a(1) =8a(2) =42a(3) =188a(4) =787a(5) =3204a(6) =12900a(7) =51720a(8) =207045a(9) =828400a(10) =3313886a(11) =13255908a(12) =53024087a(13) =212096908a(14) =848388312a(15) =3393554064a(16) =13574217225a(17) =54296870040a(18) =217187481490a(19) =868749927500