OFFSET
0,1
COMMENTS
a(n)^2 - 3*b(n)^2 = 13, with the companion sequence b(n)= A077237(n).
Positive values of x (or y) satisfying x^2 - 4xy + y^2 + 39 = 0. - Colin Barker, Feb 06 2014
Positive values of x (or y) satisfying x^2 - 14xy + y^2 + 624 = 0. - Colin Barker, Feb 16 2014
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,4,0,-1).
FORMULA
G.f.: (1-x)*(4+9*x+4*x^2)/(1-4*x^2+x^4).
a(n) = 4*a(n-2)-a(n-4). - Colin Barker, Feb 06 2014
EXAMPLE
11 = a(2) = sqrt(3*A077237(2)^2 + 13) = sqrt(3*6^2 + 13)= sqrt(121) = 11.
MATHEMATICA
CoefficientList[Series[(1 - x) (4 + 9 x + 4 x^2)/(1 - 4 x^2 + x^4), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 07 2014 *)
LinearRecurrence[{0, 4, 0, -1}, {4, 5, 11, 16}, 40] (* Harvey P. Dale, Oct 23 2015 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Nov 08 2002
EXTENSIONS
More terms from Colin Barker, Feb 06 2014
STATUS
approved