OFFSET
0,1
COMMENTS
For more information about this type of recurrence follow the Khovanova link and see A086902 and A054413. - Johannes W. Meijer, Jun 12 2010
LINKS
FORMULA
a(n) = ((13+sqrt(173))/2)^n + ((13-sqrt(173))/2)^n.
Lim_{n -> oo} a(n+1)/a(n) = (13 + sqrt(173))/2.
Lim_{n -> oo} a(n)/a(n+1) = 2/(13+sqrt(173)).
G.f.: (2-13*x)/(1-13*x-x^2). - Philippe Deléham, Nov 02 2008
From Johannes W. Meijer, Jun 12 2010: (Start)
a(2*n+1) = 13*A097845(n).
MATHEMATICA
LinearRecurrence[{13, 1}, {2, 13}, 31] (* Stefano Spezia, Sep 20 2022 *)
PROG
(Magma) I:=[2, 13]; [n le 2 select I[n] else 13*Self(n-1) +Self(n-2): n in [1..31]]; // G. C. Greubel, Dec 13 2022
(SageMath)
A088316=BinaryRecurrenceSequence(13, 1, 2, 13)
[A088316(n) for n in range(31)] # G. C. Greubel, Dec 13 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Nikolay V. Kosinov, Dmitry V. Polyakov (kosinov(AT)unitron.com.ua), Nov 06 2003
STATUS
approved