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) =2a(3) =4a(4) =7a(5) =13a(6) =22a(7) =37a(8) =61a(9) =101a(10) =165a(11) =269a(12) =437a(13) =710a(14) =1151a(15) =1865a(16) =3020a(17) =4890a(18) =7915a(19) =12810a(20) =20730a(21) =33546a(22) =54282a(23) =87834a(24) =142122a(25) =229963a(26) =372092a(27) =602062a(28) =974161a(29) =1576231