a(n) = (4^n + 15*n - 1)/9.

Terms

a(0) =0a(1) =2a(2) =5a(3) =12a(4) =35a(5) =122a(6) =465a(7) =1832a(8) =7295a(9) =29142a(10) =116525a(11) =466052a(12) =1864155a(13) =7456562a(14) =29826185a(15) =119304672a(16) =477218615a(17) =1908874382a(18) =7635497445a(19) =30541989692a(20) =122167958675a(21) =488671834602