Number of binary strings of length n with no substrings equal to 0001 or 0101.

Terms

a(0) =1a(1) =2a(2) =4a(3) =8a(4) =14a(5) =24a(6) =42a(7) =72a(8) =122a(9) =208a(10) =354a(11) =600a(12) =1018a(13) =1728a(14) =2930a(15) =4968a(16) =8426a(17) =14288a(18) =24226a(19) =41080a(20) =69658a(21) =118112a(22) =200274a(23) =339592a(24) =575818a(25) =976368a(26) =1655554a(27) =2807192a(28) =4759930a(29) =8071040