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

Terms

a(0) =0a(1) =1a(2) =5a(3) =11a(4) =22a(5) =40a(6) =70a(7) =119a(8) =199a(9) =329a(10) =540a(11) =882a(12) =1436a(13) =2333a(14) =3785a(15) =6135a(16) =9938a(17) =16092a(18) =26050a(19) =42163a(20) =68235a(21) =110421a(22) =178680a(23) =289126a(24) =467832a(25) =756985a(26) =1224845a(27) =1981859a(28) =3206734a(29) =5188624