OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (10,-22).
FORMULA
From Emeric Deutsch, Jul 05 2009: (Start)
G.f.: (1 - 2*x)/(1 - 10*x + 22*x^2).
a(n) = 10*a(n-1) - 22*a(n-2) for n >= 2; a(0)=1, a(1)=8. (End)
E.g.f.: exp(5*x)*(cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x)). - Stefano Spezia, Dec 31 2022
MAPLE
seq(expand(((1+sqrt(3))*(5+sqrt(3))^n+(1-sqrt(3))*(5-sqrt(3))^n)*1/2), n = 0 .. 20); # Emeric Deutsch, Jul 05 2009
MATHEMATICA
LinearRecurrence[{10, -22}, {1, 8}, 40] (* Vincenzo Librandi, Feb 03 2018 *)
PROG
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-3); S:=[ ((1+r)*(5+r)^n+(1-r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 02 2009
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Jun 29 2009
EXTENSIONS
Edited and extended beyond a(5) by Klaus Brockhaus, Jul 05 2009
Extended by Emeric Deutsch, Jul 05 2009
STATUS
approved