Number of compositions of n with parts in N which avoid the consecutive pattern 123.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =8a(5) =16a(6) =31a(7) =61a(8) =119a(9) =232a(10) =453a(11) =883a(12) =1721a(13) =3354a(14) =6536a(15) =12735a(16) =24813a(17) =48344a(18) =94189a(19) =183506a(20) =357518a(21) =696534a(22) =1357019a(23) =2643798a(24) =5150746a(25) =10034865a(26) =19550268a(27) =38088486a(28) =74205248a(29) =144569092