a(n) = Sum_{k=0..n} 3^(n-k) * floor(k/3).

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =4a(5) =13a(6) =41a(7) =125a(8) =377a(9) =1134a(10) =3405a(11) =10218a(12) =30658a(13) =91978a(14) =275938a(15) =827819a(16) =2483462a(17) =7450391a(18) =22351179a(19) =67053543a(20) =201160635a(21) =603481912a(22) =1810445743a(23) =5431337236a(24) =16294011716a(25) =48882035156a(26) =146646105476a(27) =439938316437