A B2-sequence due to Rachel Lewis.

Terms

a(0) =1a(1) =2a(2) =4a(3) =8a(4) =13a(5) =21a(6) =31a(7) =45a(8) =66a(9) =81a(10) =97a(11) =123a(12) =148a(13) =182a(14) =204a(15) =252a(16) =291a(17) =324a(18) =352a(19) =415a(20) =486a(21) =540a(22) =651a(23) =706a(24) =781a(25) =864a(26) =963a(27) =1003a(28) =1148a(29) =1217