OFFSET
0,2
COMMENTS
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (8, -14).
FORMULA
a(n) = 8*a(n-1) - 14*a(n-2) for n > 1; a(0) = 1, a(1) = 6.
a(n) = ((1+sqrt(2))*(4+sqrt(2))^n+(1-sqrt(2))*(4-sqrt(2))^n)/2.
G.f.: (1-2*x)/(1-8*x+14*x^2).
E.g.f.: exp(4*x)*( cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Dec 19 2016
MATHEMATICA
LinearRecurrence[{8, -14}, {1, 6}, 30] (* Harvey P. Dale, May 08 2014 *)
PROG
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+r)*(4+r)^n+(1-r)*(4-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 26 2009
(PARI) Vec((1-2*x)/(1-8*x+14*x^2) + O(x^50)) \\ G. C. Greubel, Dec 19 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Jul 25 2009
EXTENSIONS
Edited and extended beyond a(5) by Klaus Brockhaus, Jul 26 2009
New name from G. C. Greubel, Dec 19 2016
STATUS
approved