(1/3) times the sum of the elements of all subsets of [n] whose sum is divisible by three.

Terms

a(0) =0a(1) =0a(2) =1a(3) =4a(4) =9a(5) =30a(6) =84a(7) =202a(8) =528a(9) =1320a(10) =3144a(11) =7568a(12) =17888a(13) =41472a(14) =95760a(15) =218880a(16) =495344a(17) =1114656a(18) =2491584a(19) =5534688a(20) =12234880a(21) =26916736a(22) =58954752a(23) =128629248a(24) =279628800a(25) =605847808a(26) =1308632832a(27) =2818593792a(28) =6054720768a(29) =12974405120