OFFSET
0,2
COMMENTS
All numbers are odd.
LINKS
Olimpiada Matemática Española, Si n es un número natural, demostrar que la parte entera de (4 + sqrt(11))^n es un número impar (in Spanish), Problem 26/3 (1990), page 26.
Index entries for linear recurrences with constant coefficients, signature (9,-13,5).
FORMULA
O.g.f.: (1 - 2*x + 3*x^2)/((1 - x)*(1 - 8*x + 5*x^2)). - Ilya Gutkovskiy, Dec 13 2016
E.g.f.: exp((4 + sqrt(11))*x) + exp((4 - sqrt(11))*x) - exp(x). - Bruno Berselli, Dec 14 2016
a(n) = 9*a(n-1) - 13*a(n-2) + 5*a(n-3) for n>2.
a(n) = 8*a(n-1) - 5*a(n-2) + 2 for n>1.
a(n) = (4 + sqrt(11))^n + (4 - sqrt(11))^n - 1. - Bruno Berselli, Dec 13 2016
MATHEMATICA
Floor[(4+Sqrt[11])^Range[0, 30]] (* or *) LinearRecurrence[{9, -13, 5}, {1, 7, 53}, 30] (* Harvey P. Dale, Apr 22 2019 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Philippe Deléham, Dec 13 2016
STATUS
approved