OFFSET
0,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-2).
FORMULA
a(n) = 4*a(n-1) - 2*a(n-2) for n > 1; a(0) = 1, a(1) = 8.
G.f.: (1+4*x)/(1-4*x+2*x^2).
E.g.f.: exp(2*x)*( cosh(sqrt(2)*x) + 3*sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Jul 30 2017
MATHEMATICA
LinearRecurrence[{4, -2}, {1, 8}, 50] (* G. C. Greubel, Jul 30 2017 *)
PROG
(Magma) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+3*r)*(2+r)^n+(1-3*r)*(2-r)^n)/2: n in [0..23] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 06 2009
(PARI) x='x+O('x^50); Vec((1+4*x)/(1-4*x+2*x^2)) \\ G. C. Greubel, Jul 30 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Aug 01 2009
EXTENSIONS
Edited and extended beyond a(5) by Klaus Brockhaus, Aug 06 2009
STATUS
approved