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 (8,-5).
FORMULA
a(n) = ((4 + sqrt(11))^n - (4 - sqrt(11))^n)/(2*sqrt(11)). - Giorgio Balzarotti, May 28 2011
G.f.: x/(1 - 8*x + 5*x^2). - Philippe Deléham, Oct 12 2011
From G. C. Greubel, Jun 17 2022: (Start)
a(n) = 5^((n-1)/2)*ChebyshevU(n-1, 4/sqrt(5)).
E.g.f.: (1/sqrt(11))*exp(4*x)*sinh(sqrt(11)*x). (End)
MATHEMATICA
LinearRecurrence[{8, -5}, {0, 1}, 50]
PROG
(Magma) [n le 2 select n-1 else 8*Self(n-1) -5*Self(n-2): n in [1..41]]; // G. C. Greubel, Jun 17 2022
(SageMath) [sum( (-1)^k*binomial(n-k-1, k)*5^k*8^(n-2*k-1) for k in (0..((n-1)//2))) for n in (0..40)] # G. C. Greubel, Jun 17 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Joseph Stephan Orlovsky, May 24 2011
STATUS
approved