Q-toothpick sequence (see Comments for precise definition).

Terms

a(0) =0a(1) =1a(2) =5a(3) =12a(4) =24a(5) =46a(6) =66a(7) =88a(8) =128a(9) =182a(10) =222a(11) =244a(12) =284a(13) =338a(14) =394a(15) =464a(16) =584a(17) =718a(18) =790a(19) =812a(20) =852a(21) =906a(22) =962a(23) =1032a(24) =1152a(25) =1286a(26) =1374a(27) =1444a(28) =1564a(29) =1714