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,-11).
FORMULA
a(n) = 8*a(n-1) - 11*a(n-2) for n > 1; a(0) = 3, a(1) = 17.
G.f.: (3-7*x)/(1-8*x+11*x^2).
MATHEMATICA
CoefficientList[Series[(3-7*x)/(1-8*x+11*x^2), {x, 0, 50}], x] (* or *) LinearRecurrence[{8, -11}, {3, 17}, 30] (* G. C. Greubel, Dec 22 2017 *)
PROG
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-5); S:=[ ((3+r)*(4+r)^n+(3-r)*(4-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 21 2009
(Magma) I:=[3, 17]; [n le 2 select I[n] else 8*Self(n-1) - 11*Self(n-2): n in [1..30]]; // G. C. Greubel, Dec 22 2017
(PARI) x='x+O('x^30); Vec((3-7*x)/(1-8*x+11*x^2)) \\ G. C. Greubel, Dec 22 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Jul 20 2009
EXTENSIONS
Edited and extended beyond a(5) by Klaus Brockhaus, Jul 21 2009
STATUS
approved