a(n) is the number of ternary strings of length n with at least three 0's.

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =9a(5) =51a(6) =233a(7) =939a(8) =3489a(9) =12259a(10) =41385a(11) =135675a(12) =435185a(13) =1373139a(14) =4279161a(15) =13210219a(16) =40490817a(17) =123438531a(18) =374772041a(19) =1134343131a(20) =3425442705a(21) =10326135475a(22) =31088506905a(23) =93507741771a(24) =281053804769a(25) =844319042211