Let X denote the 2 X 2 matrix [0,1; 1,exp(1)], let Y = X^n; a(n) = floor(Y[1,1]).

Terms

a(0) =0a(1) =1a(2) =2a(3) =8a(4) =25a(5) =77a(6) =236a(7) =721a(8) =2198a(9) =6698a(10) =20408a(11) =62173a(12) =189414a(13) =577055a(14) =1758012a(15) =5355828a(16) =16316664a(17) =49709120a(18) =151440064a(19) =461365896a(20) =1405562597a(21) =4282081163a(22) =13045466011a(23) =39743334364a(24) =121079049617a(25) =168870314746