A138804 Let X denote the 2 X 2 matrix [0,1; 1,exp(1)], let Y = X^n; a(n) = floor(Y[1,1]).

0, 1, 2, 8, 25, 77, 236, 721, 2198, 6698, 20408, 62173, 189414, 577055, 1758012, 5355828, 16316664, 49709120, 151440064, 461365896, 1405562597, 4282081163, 13045466011, 39743334364, 121079049617, 168870314746

Offset

1,3

Comments

a(n)/a(n-1) tends to 3.046524695... = exp ArcSinh(e/2) = (exp(1)+(exp(2)+4)^(1/2))/2, the largest eigenvalue of X.

Links

Table of n, a(n) for n=1..26.

Example

a(5) = 5 floor of term (1,1) in X^5 = 25.

Maple

ans:=[];
A:=Matrix(2, 2, [[0, 1], [1, exp(1)]]);
B:=Matrix(2, 2, [[0, 1], [1, exp(1)]]);
for n from 1 to 20 do
ans:=[op(ans), floor(B[1, 1])];
B:=A.B;
od:
ans; # N. J. A. Sloane, Jul 01 2017

Crossrefs

Sequence in context: A176855 A309237 A037560 * A212323 A301842 A240478

Adjacent sequences: A138801 A138802 A138803 * A138805 A138806 A138807

Keyword

nonn

Author

Gary W. Adamson, Mar 30 2008

Extensions

Definition corrected by N. J. A. Sloane, Jul 01 2017

Status

approved