A098706 a(n) = 2*A076218(n).

0, 2, 10, 290, 9802, 332930, 11309770, 384199202, 13051463050, 443365544450, 15061377048202, 511643454094370, 17380816062160330, 590436102659356802, 20057446674355970890, 681362750825443653410, 23146276081390728245002, 786292024016459316676610

Offset: 0

Author

Charlie Marion, Oct 28 2004

Keywords

• nonn
• easy

Examples

			a(3) = 2*5*29 = 2*145.
		

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).

Programs

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 *)

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

Formula

a(0)=0, a(1)=2, and a(n) = 2*A001653(n-2) * A001653(n-1) for n>=2.

For n>1, a(n) = A002315(n-2)*A002315(n-1) + 3.

For n>0, a(n) = (A001542(n-1)-1)^2 + (A001542(n-1)-1)^2.

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)

Extensions

More terms from Ray Chandler, Nov 10 2004