OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..144 from Vincenzo Librandi)
Index entries for linear recurrences with constant coefficients, signature (10, -17).
FORMULA
a(n) = 10*a(n-1) - 17*a(n-2) for n > 1; a(0) = 1, a(1) = 21.
a(n) = ((1+4*sqrt(2))*(5+2*sqrt(2))^n + (1-4*sqrt(2))*(5-2*sqrt(2))^n)/2.
G.f.: (1+11*x)/(1-10*x+17*x^2).
E.g.f.: exp(5*x)*(cosh(2*sqrt(2)*x) + 4*sqrt(2)*sinh(2*sqrt(2)*x)). - G. C. Greubel, Aug 10 2017
MATHEMATICA
LinearRecurrence[{10, -17}, {1, 21}, 30] (* Harvey P. Dale, May 22 2013 *)
PROG
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+4*r)*(5+2*r)^n+(1-4*r)*(5-2*r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 23 2009
(PARI) x='x+O('x^50); Vec((1+11*x)/(1-10*x+17*x^2)) \\ G. C. Greubel, Aug 10 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Aug 17 2009
EXTENSIONS
Edited and extended beyond a(5) by Klaus Brockhaus, Aug 23 2009
STATUS
approved