Power floor-ceiling sequence of 2+sqrt(2).

Terms

a(0) =3a(1) =11a(2) =37a(3) =127a(4) =433a(5) =1479a(6) =5049a(7) =17239a(8) =58857a(9) =200951a(10) =686089a(11) =2342455a(12) =7997641a(13) =27305655a(14) =93227337a(15) =318298039a(16) =1086737481a(17) =3710353847a(18) =12667940425a(19) =43251054007a(20) =147668335177a(21) =504171232695