Number of distinct bags of distinct sequences of 1s and 2s such that the sum of all terms is n.

Terms

a(0) =1a(1) =1a(2) =3a(3) =6a(4) =14a(5) =28a(6) =61a(7) =122a(8) =253a(9) =505a(10) =1017a(11) =2008a(12) =3976a(13) =7769a(14) =15169a(15) =29379a(16) =56751a(17) =108993a(18) =208725a(19) =397913a(20) =756385a(21) =1432578a(22) =2705744a(23) =5094749a(24) =9568504a(25) =17922756a(26) =33492061a(27) =62438472a(28) =116151352a(29) =215612548