Descending dungeons: for definition see Comments lines.

Terms

a(0) =10a(1) =11a(2) =13a(3) =16a(4) =20a(5) =25a(6) =31a(7) =38a(8) =46a(9) =55a(10) =110a(11) =221a(12) =444a(13) =891a(14) =1786a(15) =3577a(16) =7160a(17) =14327a(18) =28662a(19) =57333a(20) =171999a(21) =515998a(22) =1547996a(23) =4643991a(24) =13931977a(25) =41795936a(26) =125387814a(27) =376163449a(28) =1128490355a(29) =3385471074