OFFSET
0,2
LINKS
Colin Barker, Table of n, a(n) for n = 0..650
Hacène Belbachir, Soumeya Merwa Tebtoub, and László Németh, Ellipse Chains and Associated Sequences, J. Int. Seq., Vol. 23 (2020), Article 20.8.5.
Soumeya M. Tebtoub, Hacène Belbachir, and László Németh, Integer sequences and ellipse chains inside a hyperbola, Proceedings of the 1st International Conference on Algebras, Graphs and Ordered Sets (ALGOS 2020), hal-02918958 [math.cs], 17-18.
Index entries for linear recurrences with constant coefficients, signature (35,-35,1).
FORMULA
From Colin Barker, Mar 02 2016: (Start)
a(n) = (6+(17+12*sqrt(2))^(1-n)+(17-12*sqrt(2))*(17+12*sqrt(2))^n)/4 for n>0.
a(n) = 35*a(n-1)-35*a(n-2)+a(n-3) for n>3.
G.f.: 2*x*(1-30*x+5*x^2) / ((1-x)*(1-34*x+x^2)).
(End)
EXAMPLE
a(3) = 2*5*29 = 2*145.
MATHEMATICA
LinearRecurrence[{35, -35, 1}, {0, 2, 10, 290}, 18] (* or *)
CoefficientList[Series[2 x (1 - 30 x + 5 x^2)/((1 - x) (1 - 34 x + x^2)), {x, 0, 17}], x] (* Michael De Vlieger, Nov 02 2020 *)
PROG
(PARI) concat(0, Vec(2*x*(1-30*x+5*x^2)/((1-x)*(1-34*x+x^2)) + O(x^20))) \\ Colin Barker, Mar 02 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Charlie Marion, Oct 28 2004
EXTENSIONS
More terms from Ray Chandler, Nov 10 2004
STATUS
approved