OFFSET
0,1
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..100 from Vincenzo Librandi)
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) = 5, a(1) = 21.
G.f.: (5-9*x)/(1-6*x+7*x^2).
a(n) = ((5+3*sqrt(2))*(3+sqrt(2))^n+(5-3*sqrt(2))*(3-sqrt(2))^n)/2.
E.g.f.: (5*cosh(sqrt(2)*x) + 3*sqrt(2)*sinh(sqrt(2)*x))*exp(3*x). - G. C. Greubel, Sep 08 2017
MATHEMATICA
CoefficientList[Series[(5-9x)/(1-6x+7x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[{6, -7}, {5, 21}, 30] (* Harvey P. Dale, Apr 27 2017 *)
PROG
(Magma) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((5+3*r)*(3+r)^n+(5-3*r)*(3-r)^n)/2: n in [0..21] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 10 2009
(PARI) Vec((5-9*x)/(1-6*x+7*x^2)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Aug 08 2009
EXTENSIONS
Edited and extended beyond a(5) by Klaus Brockhaus, Aug 10 2009
STATUS
approved