a(n+2) = a(n+1) + a(n) + (-1)^n, with a(1) = a(2) = 1.

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =3a(5) =7a(6) =9a(7) =17a(8) =25a(9) =43a(10) =67a(11) =111a(12) =177a(13) =289a(14) =465a(15) =755a(16) =1219a(17) =1975a(18) =3193a(19) =5169a(20) =8361a(21) =13531a(22) =21891a(23) =35423a(24) =57313a(25) =92737a(26) =150049a(27) =242787a(28) =392835a(29) =635623