Number of n-length words on {0,1,2} in which 0 appears only in runs of length 2.

Terms

a(0) =1a(1) =2a(2) =5a(3) =12a(4) =28a(5) =66a(6) =156a(7) =368a(8) =868a(9) =2048a(10) =4832a(11) =11400a(12) =26896a(13) =63456a(14) =149712a(15) =353216a(16) =833344a(17) =1966112a(18) =4638656a(19) =10944000a(20) =25820224a(21) =60917760a(22) =143723520a(23) =339087488a(24) =800010496a(25) =1887468032a(26) =4453111040a(27) =10506243072a(28) =24787422208a(29) =58481066496