Number of Barlow packings with group P63/mmc(S) that repeat after 4n layers.

Terms

a(0) =1a(1) =2a(2) =3a(3) =8a(4) =15a(5) =30a(6) =63a(7) =128a(8) =252a(9) =510a(10) =1023a(11) =2040a(12) =4095a(13) =8190a(14) =16365a(15) =32768a(16) =65535a(17) =131040a(18) =262143a(19) =524280a(20) =1048509a(21) =2097150a(22) =4194303a(23) =8388480a(24) =16777200a(25) =33554430a(26) =67108608a(27) =134217720a(28) =268435455a(29) =536870370