OFFSET
0,1
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (8,-14).
FORMULA
a(n) = 8*a(n-1) - 14*a(n-2) for n > 1; a(0) = 2, a(1) = 11.
G.f.: (2-5*x)/(1-8*x+14*x^2).
E.g.f.: (2*cosh(sqrt(2)*x) + (3*sqrt(2)/2)*sinh(sqrt(2)*x))*exp(4*x). - G. C. Greubel, Sep 08 2017
MATHEMATICA
LinearRecurrence[{8, -14}, {2, 11}, 30] (* Harvey P. Dale, Aug 09 2016 *)
PROG
(Magma) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((4+3*r)*(4+r)^n+(4-3*r)*(4-r)^n)/4: n in [0..20] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 09 2009
(PARI) x='x+O('x^50); Vec((2-5*x)/(1-8*x+14*x^2)) \\ G. C. Greubel, Sep 08 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Aug 08 2009
EXTENSIONS
Edited and extended beyond a(5) by Klaus Brockhaus, Aug 09 2009
STATUS
approved