a(n) = a(n-1) + a(n-2) + k, n>1; with a(0) = 1, a(1) = 2, k = 3.

Terms

a(0) =1a(1) =2a(2) =6a(3) =11a(4) =20a(5) =34a(6) =57a(7) =94a(8) =154a(9) =251a(10) =408a(11) =662a(12) =1073a(13) =1738a(14) =2814a(15) =4555a(16) =7372a(17) =11930a(18) =19305a(19) =31238a(20) =50546a(21) =81787a(22) =132336a(23) =214126a(24) =346465a(25) =560594a(26) =907062a(27) =1467659a(28) =2374724a(29) =3842386