OFFSET
0,2
LINKS
Harry J. Smith, Table of n, a(n) for n = 0..1584
Tanya Khovanova, Recursive Sequences.
Index entries for linear recurrences with constant coefficients, signature (4,1).
FORMULA
a(n) = ( (7+sqrt(5))(2+sqrt(5))^n - (7-sqrt(5))(2-sqrt(5))^n )/2*sqrt(5).
G.f.: (1+5*x)/(1-4*x-x^2). - Philippe Deléham, Nov 03 2008
a(n) = F(3*n+3) + F(3*n-2); F = A000045. - Yomna Bakr and Greg Dresden, May 25 2024
EXAMPLE
a(n) = 4a(n-1) + a(n-2); a(0)=1, a(1)=9.
MAPLE
with(combinat): a:=n->5*fibonacci(n-1, 4)+fibonacci(n, 4): seq(a(n), n=1..16); # Zerinvary Lajos, Apr 04 2008
MATHEMATICA
LinearRecurrence[{4, 1}, {1, 9}, 31] (* or *) CoefficientList[ Series[ (1+5x)/(1-4x-x^2), {x, 0, 30}], x] (* Harvey P. Dale, Jul 12 2011 *)
PROG
(PARI) { default(realprecision, 2000); for (n=0, 2000, a=round(((7+sqrt(5))*(2+sqrt(5))^n - (7-sqrt(5))*(2-sqrt(5))^n )/10*sqrt(5)); if (a > 10^(10^3 - 6), break); write("b048878.txt", n, " ", a); ); } \\ Harry J. Smith, May 31 2009
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
STATUS
approved