OFFSET
0,1
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..169 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) = 3, a(1) = 17.
G.f.: (3-x)/(1-6*x+7*x^2).
a(n) = ((3+4*sqrt(2))*(3+sqrt(2))^n + (3-4*sqrt(2))*(3-sqrt(2))^n)/2.
E.g.f.: (3*cosh(sqrt(2)*x) + 4*sqrt(2)*sinh(sqrt(2)*x))*exp(3*x). - G. C. Greubel, Sep 13 2017
MATHEMATICA
LinearRecurrence[{6, -7}, {3, 17}, 30] (* Harvey P. Dale, Jun 03 2015 *)
PROG
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((3+4*r)*(3+r)^n+(3-4*r)*(3-r)^n)/2: n in [0..21] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 20 2009
(PARI) x='x+O('x^50); Vec((3-x)/(1-6*x+7*x^2)) \\ G. C. Greubel, Sep 13 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Aug 12 2009
EXTENSIONS
Edited and extended beyond a(5) by Klaus Brockhaus, Aug 20 2009
STATUS
approved