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) =8a(3) =20a(4) =43a(5) =82a(6) =148a(7) =257a(8) =436a(9) =728a(10) =1203a(11) =1974a(12) =3224a(13) =5249a(14) =8528a(15) =13836a(16) =22427a(17) =36330a(18) =58828a(19) =95233a(20) =154140a(21) =249456a(22) =403683a(23) =653230a(24) =1057008a(25) =1710337a(26) =2767448a(27) =4477892a(28) =7245451a(29) =11723458