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

Terms

a(0) =0a(1) =1a(2) =4a(3) =11a(4) =24a(5) =47a(6) =86a(7) =151a(8) =258a(9) =433a(10) =718a(11) =1181a(12) =1932a(13) =3149a(14) =5120a(15) =8311a(16) =13476a(17) =21835a(18) =35362a(19) =57251a(20) =92670a(21) =149981a(22) =242714a(23) =392761a(24) =635544a(25) =1028377a(26) =1663996a(27) =2692451a(28) =4356528a(29) =7049063