OFFSET
0,1
REFERENCES
Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2025.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1000
Miguel-Ángel Pérez García-Ortega, El Libro de las Ternas Pitagóricas.
Index entries for linear recurrences with constant coefficients, signature (3,0,-3,1).
FORMULA
a(n) = 2*Lucas(n)^2 - 1.
a(n) = 2*A001254(n) - 1.
G.f.: (7 - 20*x + 14*x^2 + x^3)/((1 - x)*(1 + x)*(1 - 3*x + x^2)). - Andrew Howroyd, Nov 12 2025
EXAMPLE
MATHEMATICA
a=Table[LucasL[n], {n, 0, 30}]; Apply[Join, Map[{2#^2-1}&, a]]
PROG
(PARI) a(n) = 2*(fibonacci(n+1)+fibonacci(n-1))^2 - 1 \\ Andrew Howroyd, Nov 12 2025
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Miguel-Ángel Pérez García-Ortega, Apr 13 2025
STATUS
approved