Expansion of (1+x+x^2)/((1-x^2)*(1-2*x-x^2)); a Pellian-related sequence.

Terms

a(0) =1a(1) =3a(2) =9a(3) =22a(4) =55a(5) =133a(6) =323a(7) =780a(8) =1885a(9) =4551a(10) =10989a(11) =26530a(12) =64051a(13) =154633a(14) =373319a(15) =901272a(16) =2175865a(17) =5253003a(18) =12681873a(19) =30616750a(20) =73915375a(21) =178447501a(22) =430810379a(23) =1040068260a(24) =2510946901a(25) =6061962063a(26) =14634871029a(27) =35331704122a(28) =85298279275a(29) =205928262673