OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (7,-5).
FORMULA
a(n) = ((7/2 + 1/2*sqrt(29))^n - (7/2 - 1/2*sqrt(29))^n)/sqrt(29). - Giorgio Balzarotti, May 28 2011
G.f.: x/(1 - 7*x + 5*x^2). - Philippe Deléham, Oct 12 2011
From G. C. Greubel, Jun 11 2022: (Start)
a(n) = 5^((n-1)/2)*ChebyshevU(n-1, 7/(2*sqrt(5))).
E.g.f.: (2/sqrt(29))*exp(7*x/2)*sinh(sqrt(29)*x/2). (End)
MATHEMATICA
LinearRecurrence[{7, -5}, {0, 1}, 50]
PROG
(Magma) [n le 2 select n-1 else 7*Self(n-1) - 5*Self(n-2): n in [1..51]]; // G. C. Greubel, Jun 11 2022
(SageMath) [lucas_number1(n, 7, 5) for n in (0..50)] # G. C. Greubel, Jun 11 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vladimir Joseph Stephan Orlovsky, May 24 2011
STATUS
approved