OFFSET
1,1
COMMENTS
Values of x satisfying the Pellian equation x^2 - 10*y^2 = 4.
LINKS
Colin Barker, Table of n, a(n) for n = 1..600
Hacène Belbachir, Soumeya Merwa Tebtoub, and László Németh, Ellipse Chains and Associated Sequences, J. Int. Seq., Vol. 23 (2020), Article 20.8.5.
Index entries for linear recurrences with constant coefficients, signature (38,-1).
FORMULA
a(n) = 2*A078986(n).
a(n) = (19+6*sqrt(10))^(-n)+(19+6*sqrt(10))^n.
a(n) = 38*a(n-1)-a(n-2).
G.f.: -2*x*(x-19) / (x^2-38*x+1).
EXAMPLE
1442 is in the sequence because (1442^2-4)/10 = 207936 = 456^2.
MATHEMATICA
LinearRecurrence[{38, -1}, {38, 1442}, 30] (* Harvey P. Dale, Dec 19 2014 *)
PROG
(PARI) Vec(-2*x*(x-19)/(x^2-38*x+1) + O(x^100))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Mar 17 2014
STATUS
approved