OFFSET
0,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,1).
FORMULA
a(n) = 2*a(n-1) + a(n-2) for n > 1; a(0) = 5, a(1) = 9.
G.f.: (5-x)/(1-2*x-x^2).
E.g.f.: exp(x)*( 5*cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Jul 29 2017
MATHEMATICA
LinearRecurrence[{2, 1}, {5, 9}, 50] (* G. C. Greubel, Jul 29 2017 *)
PROG
(Magma) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((5+2*r)*(1+r)^n+(5-2*r)*(1-r)^n)/2: n in [0..27] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 06 2009
(PARI) x='x+O('x^50); Vec((5-x)/(1-2*x-x^2)) \\ G. C. Greubel, Jul 29 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Aug 01 2009
EXTENSIONS
Edited and extended beyond a(5) by Klaus Brockhaus, Aug 06 2009
STATUS
approved