Royal paths in a lattice.

Terms

a(0) =1a(1) =8a(2) =48a(3) =264a(4) =1408a(5) =7432a(6) =39152a(7) =206600a(8) =1093760a(9) =5813000a(10) =31019568a(11) =166188552a(12) =893763840a(13) =4823997960a(14) =26124870640a(15) =141926904328a(16) =773293020928