OFFSET
0,3
COMMENTS
The numerators are given in A295331.
The continued fraction expansion of sqrt(13)/2 is [1, repeat(1, 4, 14, 4, 1, 2)].
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 1298, 0, 0, 0, 0, 0, -1).
FORMULA
G.f.: (1 + x + 5*x^2 + 71*x^3 + 289*x^4 + 360*x^5 - 289*x^6 + 71*x^7 - 5*x^8 + x^9 - x^10) / ((1 - 3*x - x^2)*(1 + 3*x - x^2)*(1 + 3*x + 10*x^2 - 3*x^3 + x^4)*(1 - 3*x + 10*x^2 + 3*x^3 + x^4)). See A295331 for a hint for the derivation. Here the a(n) recurrence is the same as there but the inputs are a(0) = 1, a(-1) = 0, (a(-2) = 1). The unfactorized denominator is 1 - 1298*x^6 + x^12.
a(n) = 1298*a(n-6) - a(n-12), n >= 12, with inputs a(0)..a(11).
EXAMPLE
See A295331 for the first convergents.
CROSSREFS
KEYWORD
nonn,frac,cofr,easy
AUTHOR
Wolfdieter Lang, Nov 20 2017
STATUS
approved