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) =6a(3) =17a(4) =38a(5) =75a(6) =138a(7) =243a(8) =416a(9) =699a(10) =1160a(11) =1909a(12) =3124a(13) =5093a(14) =8282a(15) =13445a(16) =21802a(17) =35327a(18) =57214a(19) =92631a(20) =149940a(21) =242671a(22) =392716a(23) =635497a(24) =1028328a(25) =1663945a(26) =2692398a(27) =4356473a(28) =7049006a(29) =11405619