OFFSET
0,1
COMMENTS
LINKS
Matthew House, Table of n, a(n) for n = 0..1542
Index entries for linear recurrences with constant coefficients, signature (6,-7).
FORMULA
a(n) = 6*a(n-1) - 7*a(n-2) for n > 1; a(0) = 2, a(1) = 9.
G.f.: (2-3*x)/(1-6*x+7*x^2).
E.g.f.: (2*cosh(sqrt(2)*x) + (3/sqrt(2))*sinh(sqrt(2)*x))*exp(3*x). - G. C. Greubel, Sep 08 2017
MATHEMATICA
CoefficientList[Series[(2-3*x)/(1-6*x+7*x^2), {x, 0, 1000}],
x] (* or *) LinearRecurrence[{6, -7}, {2, 9}, 50] (* G. C. Greubel, Sep 08 2017 *)
PROG
(Magma) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((4+3*r)*(3+r)^n+(4-3*r)*(3-r)^n)/4: n in [0..21] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 09 2009
(PARI) x='x+O('x^50); Vec((2-3*x)/(1-6*x+7*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