a(n) = Sum_{k=0..n} 4^(n-k) * floor(k/3).

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =5a(5) =21a(6) =86a(7) =346a(8) =1386a(9) =5547a(10) =22191a(11) =88767a(12) =355072a(13) =1420292a(14) =5681172a(15) =22724693a(16) =90898777a(17) =363595113a(18) =1454380458a(19) =5817521838a(20) =23270087358a(21) =93080349439a(22) =372321397763