Solution (a(n)) of the complementary equation a(n) = 2*a(n-1) - a(n-2) + b(n); see Comments.

Terms

a(0) =1a(1) =2a(2) =8a(3) =20a(4) =39a(5) =67a(6) =105a(7) =154a(8) =215a(9) =289a(10) =377a(11) =480a(12) =599a(13) =735a(14) =889a(15) =1062a(16) =1256a(17) =1472a(18) =1711a(19) =1974a(20) =2262a(21) =2576a(22) =2917a(23) =3286a(24) =3684a(25) =4112a(26) =4571a(27) =5062a(28) =5586a(29) =6144