a(0) = 0, a(1) = 1; for n > 1, a(n) = a(n-2) + a(n-1) + A000071(n+1).

Terms

a(0) =0a(1) =1a(2) =2a(3) =5a(4) =11a(5) =23a(6) =46a(7) =89a(8) =168a(9) =311a(10) =567a(11) =1021a(12) =1820a(13) =3217a(14) =5646a(15) =9849a(16) =17091a(17) =29523a(18) =50794a(19) =87081a(20) =148820a(21) =253611a(22) =431087a(23) =731065a(24) =1237176a(25) =2089633a(26) =3523226a(27) =5930669a(28) =9968123a(29) =16730831