a(n) = floor(n*t^n), where t=golden ratio=(1+sqrt(5))/2.

Terms

a(0) =1a(1) =5a(2) =12a(3) =27a(4) =55a(5) =107a(6) =203a(7) =375a(8) =684a(9) =1229a(10) =2189a(11) =3863a(12) =6773a(13) =11801a(14) =20460a(15) =35311a(16) =60707a(17) =104003a(18) =177631a(19) =302539a(20) =513996a(21) =871265a(22) =1473817a(23) =2488367a(24) =4194025a(25) =7057517a(26) =11858508a(27) =19898115a(28) =33345679a(29) =55814939