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

Terms

a(0) =2a(1) =0a(2) =3a(3) =1a(4) =8a(5) =8a(6) =28a(7) =43a(8) =111a(9) =204a(10) =466a(11) =924a(12) =2007a(13) =4109a(14) =8740a(15) =18136a(16) =38240a(17) =79799a(18) =167643a(19) =350664a(20) =735554a(21) =1540104a(22) =3228459a(23) =6762553a(24) =14172272a(25) =29691368a(26) =62217172a(27) =130356451a(28) =273144327a(29) =572305140