Total number of consecutive triples matching the pattern 123 in all faro permutations of length n.

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =4a(5) =10a(6) =24a(7) =53a(8) =116a(9) =246a(10) =520a(11) =1082a(12) =2248a(13) =4628a(14) =9520a(15) =19469a(16) =39796a(17) =81022a(18) =164904a(19) =334670a(20) =679064a(21) =1374924a(22) =2783440a(23) =5625666a(24) =11368904a(25) =22945820a(26) =46307664a(27) =93358228a(28) =188202256a(29) =379078952