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) =6a(3) =16a(4) =35a(5) =68a(6) =124a(7) =217a(8) =370a(9) =620a(10) =1027a(11) =1688a(12) =2760a(13) =4497a(14) =7310a(15) =11864a(16) =19235a(17) =31164a(18) =50468a(19) =81705a(20) =132250a(21) =214036a(22) =346371a(23) =560496a(24) =906960a(25) =1467553a(26) =2374614a(27) =3842272a(28) =6216995a(29) =10059380