OFFSET
0,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..151
Index entries for linear recurrences with constant coefficients, signature (10,-23).
FORMULA
a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 5, a(1) = 33.
G.f.: (5-17*x)/(1-10*x+23*x^2).
a(n) = ((5+4*sqrt(2))*(5+sqrt(2))^n + (5-4*sqrt(2))*(5-sqrt(2))^n)/2.
MATHEMATICA
LinearRecurrence[{10, -23}, {5, 33}, 20] (* Harvey P. Dale, May 29 2019 *)
PROG
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((5+4*r)*(5+r)^n+(5-4*r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 21 2009
(PARI) Vec((5-17*x)/(1-10*x+23*x^2)+O(x^99)) \\ Charles R Greathouse IV, Jun 14 2011
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 21 2009
STATUS
approved