OFFSET
0,3
COMMENTS
The numerators are given in A295333. There details are given.
LINKS
Robert Israel, Table of n, a(n) for n = 0..3795
Index entries for linear recurrences with constant coefficients, signature (0, 0, 6, 0, 0, 1).
FORMULA
G.f.: G(x) = (1 + x + 2*x^2 - x^3 + x^4)/(1 - 6*x^3 - x^6), For the derivation see A295333, but here the input of the recurrence is a(0) = 1, a(-1) = 0 (a(-2) = a(0) = 1). This leads here to G_0 = 1+ 2*x*G_2 + x*G_1, G_1 = G_0 + x*G_2, G_2 = G_1 + G_0 and the solution gives G(x).
a(n) = 6*a(n-3) + a(n-6), n >= 6, with inputs a(0)..a(5).
EXAMPLE
For the first convergents see A295333.
MAPLE
numtheory:-cfrac(sqrt(5/2), 100, 'con'):
map(denom, con[1..-2]); # Robert Israel, Nov 22 2017
MATHEMATICA
Denominator[Convergents[Sqrt[5/2], 50]] (* Wesley Ivan Hurt, Nov 21 2017 *)
CROSSREFS
KEYWORD
nonn,frac,cofr,easy
AUTHOR
Wolfdieter Lang, Nov 21 2017
STATUS
approved