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

Terms

a(0) =4a(1) =13a(2) =45a(3) =153a(4) =523a(5) =1785a(6) =6095a(7) =20809a(8) =71047a(9) =242569a(10) =828183a(11) =2827593a(12) =9654007a(13) =32960841a(14) =112535351a(15) =384219721a(16) =1311808183a(17) =4478793289a(18) =15291556791a(19) =52208640585a(20) =178251448759a(21) =608588513865