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

0,2

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

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)

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

Sequence in context: A003047 A028580 A171873 * A143249 A161181 A073834

Adjacent sequences: A098703 A098704 A098705 * A098707 A098708 A098709

Keyword

nonn,easy

Author

Charlie Marion, Oct 28 2004

Extensions

More terms from Ray Chandler, Nov 10 2004

Status

approved