Number of strings of n numbers x(i) in -1..1 with sums of x(i) and of x(i)*x(i+1) both zero.

Terms

a(0) =1a(1) =1a(2) =3a(3) =7a(4) =21a(5) =45a(6) =121a(7) =261a(8) =723a(9) =1723a(10) =5087a(11) =13091a(12) =38641a(13) =101993a(14) =297423a(15) =800187a(16) =2324961a(17) =6378601a(18) =18544345a(19) =51670725a(20) =150172263a(21) =422922591a(22) =1228542913a(23) =3488055573a(24) =10134018375a(25) =28962183951a(26) =84203226523a(27) =241924870591