OFFSET
1,2
COMMENTS
Given explicitly as the denominators of the convergents to the continued fractions
[2,(1,1,1,4)^i,5,(1,1,1,4)^{i-1},1,2] (for n odd and i = (n-1)/2)
and
[2,(1,1,1,4)^i,1,1,2,(1,4,1,1)^i,1] (for n even and i = n/2 - 1).
REFERENCES
E.-A. Majol, Note #2228, L'Intermédiaire des Mathématiciens, 9 (1902), pp. 183-185. - N. J. A. Sloane, Mar 02 2022
LINKS
Colin Barker, Table of n, a(n) for n = 1..832
Index entries for linear recurrences with constant coefficients, signature (0,254,0,-1).
FORMULA
Recurrence: a(n) = 255*a(n-2) - 255*a(n-4) + a(n-6).
From Colin Barker, Dec 11 2017: (Start)
G.f.: x*(1-x)*(1+8*x+x^2) / ((1-16*x+x^2)*(1+16*x+x^2)).
a(n) = 254*a(n-2) - a(n-4) for n>4.
(End)
EXAMPLE
For n = 3 the pair is (x,y) = (653,247).
PROG
(PARI) Vec(x*(1-x)*(1+8*x+x^2) / ((1-16*x+x^2)*(1+16*x+x^2)) + O(x^30)) \\ Colin Barker, Dec 13 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jeffrey Shallit, Dec 11 2017
STATUS
approved