Maximal number of segments (equivalently, corners) in a rook circuit of a 2n X 2n board.

Terms

a(0) =1a(1) =4a(2) =12a(3) =28a(4) =56a(5) =88a(6) =132a(7) =180a(8) =240a(9) =304a(10) =380a(11) =460a(12) =552a(13) =648a(14) =756a(15) =868a(16) =992a(17) =1120a(18) =1260a(19) =1404a(20) =1560a(21) =1720a(22) =1892a(23) =2068a(24) =2256a(25) =2448a(26) =2652a(27) =2860a(28) =3080a(29) =3304