a(n) = floor(((1+sqrt(n))/2)^n).

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =5a(5) =11a(6) =26a(7) =66a(8) =180a(9) =512a(10) =1524a(11) =4734a(12) =15291a(13) =51200a(14) =177256a(15) =633102a(16) =2328306a(17) =8801492a(18) =34147724a(19) =135789397a(20) =552761344a(21) =2300896695a(22) =9783811169a(23) =42459259013a(24) =187899387609a(25) =847288609443