Constant term of the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.

Terms

a(0) =1a(1) =3a(2) =5a(3) =10a(4) =17a(5) =28a(6) =47a(7) =76a(8) =125a(9) =203a(10) =329a(11) =534a(12) =865a(13) =1400a(14) =2267a(15) =3668a(16) =5937a(17) =9607a(18) =15545a(19) =25154a(20) =40700a(21) =65856a(22) =106558a(23) =172415a(24) =278975a(25) =451392a(26) =730368a(27) =1181762a(28) =1912131a(29) =3093895