Number of compositions of n such that no part equals any of its two immediate predecessors.

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =3a(5) =5a(6) =11a(7) =15a(8) =23a(9) =37a(10) =67a(11) =101a(12) =165a(13) =265a(14) =419a(15) =691a(16) =1123a(17) =1789a(18) =2909a(19) =4657a(20) =7515a(21) =12183a(22) =19657a(23) =31635a(24) =51101a(25) =82449a(26) =132989a(27) =214623a(28) =346485a(29) =558587