OFFSET
1,2
COMMENTS
The corresponding values of x of this Pell equation are in A056771.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..200
Hacène Belbachir, Soumeya Merwa Tebtoub, and László Németh, Ellipse Chains and Associated Sequences, J. Int. Seq., Vol. 23 (2020), Article 20.8.5.
Lisa Carbone and Pranav Shankar, Kac-Moody Fibonacci sequences, arXiv:2601.00958 [math.NT], 2026. See p. 15, Table 9.
Index entries for linear recurrences with constant coefficients, signature (34,-1).
FORMULA
a(n) = 34*a(n-1)-a(n-2) with a(1)=0, a(2)=4.
G.f.: 4*x^2/(1-34*x+x^2).
a(n) = (1/3)*A001542(2n-2). - Bruno Berselli, Dec 19 2011
MATHEMATICA
LinearRecurrence[{34, -1}, {0, 4}, 30]
With[{c=6*Sqrt[2]}, Table[((17-2c)^n-(17+2c)^n)/-c, {n, 0, 20}]]//Simplify (* Harvey P. Dale, Dec 16 2024 *)
PROG
(Magma) I:=[0, 4]; [n le 2 select I[n] else 34*Self(n-1)-Self(n-2): n in [1..20]];
(Maxima) makelist(expand(((3+2*sqrt(2))^(2*n-2)-(3-2*sqrt(2))^(2*n-2))/(6*sqrt(2))), n, 1, 18); /* Bruno Berselli, Dec 19 2011 */
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Dec 18 2011
STATUS
approved