OFFSET
0,1
LINKS
Stefano Spezia, Table of n, a(n) for n = 0..1700
Yurii S. Bystryk, Vitalii L. Denysenko, and Volodymyr I. Ostryk, Lune and Lens Sequences, ResearchGate preprint, 2024. See pp. 53, 56.
Index entries for linear recurrences with constant coefficients, signature (5,-5,1).
FORMULA
a(n) = ((2+sqrt(3))^n+(2-sqrt(3))^n)/2.
a(n) = A001075(n)+1.
From R. J. Mathar, Aug 07 2008: (Start)
a(n) = A102206(n-1).
G.f.: (1-3*x)*(x-2)/((x-1)*(x^2-4*x+1)). (End)
a(n) = 5*a(n-1) - 5*a(n-2) + a(n-3). - Wesley Ivan Hurt, Jan 16 2024
E.g.f.: cosh(x) + exp(2*x)*cosh(sqrt(3)*x) + sinh(x). - Stefano Spezia, Jul 09 2025
MATHEMATICA
Table[((-1+Sqrt[3])^n+(1+Sqrt[3])^n)^2/(2^(n+1)), {n, 0, 25}]
LinearRecurrence[{5, -5, 1}, {2, 3, 8}, 25] (* Ray Chandler, Jan 27 2014 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Zak Seidov, Sep 06 2006
STATUS
approved