OFFSET
0,2
COMMENTS
Binomial transform of A084130.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (10,-17).
FORMULA
a(n) = (5+sqrt(8))^n/2 + (5-sqrt(8))^n/2.
G.f.: (1-5*x)/(1-10*x+17*x^2).
E.g.f.: exp(5*x)*cosh(sqrt(8)*x).
a(n) = 17^((n-1)/2)*( sqrt(17)*ChebyshevU(n, 5/sqrt(17)) - 5*ChebyshevU(n-1, 5/sqrt(17)) ). - G. C. Greubel, Oct 13 2022
MATHEMATICA
LinearRecurrence[{10, -17}, {1, 5}, 20] (* Harvey P. Dale, Apr 04 2021 *)
PROG
(Magma) [n le 2 select 5^(n-1) else 10*Self(n-1) -17*Self(n-2): n in [1..41]]; // G. C. Greubel, Oct 13 2022
(SageMath)
A084131=BinaryRecurrenceSequence(10, -17, 1, 5)
[A084131(n) for n in range(41)] # G. C. Greubel, Oct 13 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 16 2003
STATUS
approved