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

Terms

a(0) =1a(1) =8a(2) =39a(3) =152a(4) =526a(5) =1704a(6) =5322a(7) =16296a(8) =49383a(9) =148864a(10) =447593a(11) =1344144a(12) =4034252a(13) =12105136a(14) =36318468a(15) =108959280a(16) =326882685a(17) =980654040a(18) =2941969435a(19) =8825917160a(20) =26477762106a(21) =79433298968a(22) =238299911854a(23) =714899753112