OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..144
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) = 11.
a(n) = ((2+3*sqrt(2))*(5+2*sqrt(2))^n + (2-3*sqrt(2))*(5-2*sqrt(2))^n)/4.
G.f.: (1+x)/(1 - 10*x + 17*x^2).
a(n) = (17)^((n-1)/2)*(sqrt(17)*ChebyshevU(n, 5/sqrt(17)) + ChebyshevU(n-1, 5/sqrt(17))). - G. C. Greubel, Jul 17 2021
MATHEMATICA
LinearRecurrence[{10, -17}, {1, 11}, 30] (* Harvey P. Dale, Jun 04 2012 *)
PROG
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((2+3*r)*(5+2*r)^n+(2-3*r)*(5-2*r)^n)/4: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 19 2009
(Sage) [(17)^((n-1)/2)*(sqrt(17)*chebyshev_U(n, 5/sqrt(17)) + chebyshev_U(n-1, 5/sqrt(17))) for n in (0..30)] # G. C. Greubel, Jul 17 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Aug 15 2009
EXTENSIONS
Edited and extended beyond a(5) by Klaus Brockhaus, Aug 19 2009
STATUS
approved