OFFSET
1,2
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (4, 6).
FORMULA
a(n)/a(n-1) tends to (2 + sqrt(10)) = 5.16227766... (a root of x^2 - 4*x - 6 and an eigenvalue of the matrix).
a(n) mod 9 == 1.
From the characteristic polynomial of the matrix we get g.f.: (6*x + 1)/(-6*x^2 - 4*x + 1), with roots a=-(2+sqrt(10))/6, b=-(2-sqrt(10))/6. Let A=3+3*sqrt(10)/10 and B=3-3*sqrt(10)/10. Then a(n) = (A*(1/a)^n + B*(1/b)^n)/6. - Lambert Herrgesell (zero815(AT)googlemail.com), Apr 04 2008
EXAMPLE
a(4) = 244 = 4*46 + 6*10 = 4*a(3) + 6*a(2).
a(4) = 244 = upper left term in [1,3; 3,3]^4.
MATHEMATICA
a = {1, 10}; Do[AppendTo[a, 4*a[[ -1]] + 6*a[[ -2]]], {25}]; a (* Stefan Steinerberger *)
LinearRecurrence[{4, 6}, {1, 10}, 30] (* Harvey P. Dale, Mar 09 2014 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Gary W. Adamson, Mar 02 2008
EXTENSIONS
More terms from Stefan Steinerberger and R. J. Mathar, Mar 02 2008
Definition corrected by Paolo P. Lava, Jun 03 2008
STATUS
approved