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a(0)=1, a(1)=7, a(n) = 42*a(n-2) - a(n-1).
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%I #16 Sep 08 2022 08:45:47

%S 1,7,35,259,1211,9667,41195,364819,1365371,13957027,43388555,

%T 542806579,1279512731,21518363587,32221171115,871550099539,

%U 481739087291,36123365093347,-15890323427125,1533071657347699,-2200465241286949

%N a(0)=1, a(1)=7, a(n) = 42*a(n-2) - a(n-1).

%C a(n)/a(n-1) tends to -7.

%H G. C. Greubel, <a href="/A165505/b165505.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-1,42).

%F G.f.: (1+8*x)/(1+x-42*x^2).

%F a(n) = Sum_{k=0..n} A112555(n,k)*6^k.

%F a(n) = (14*6^n-(-7)^n)/13. - _Klaus Brockhaus_, Sep 26 2009

%F E.g.f.: (14*exp(6*x) - exp(-7*x))/13. - _G. C. Greubel_, Oct 20 2018

%p A165505:=n->(14*6^n-(-7)^n)/13: seq(A165505(n), n=0..30); # _Wesley Ivan Hurt_, Apr 14 2017

%t LinearRecurrence[{-1, 42}, {1, 7}, 40] (* _G. C. Greubel_, Oct 20 2018 *)

%o (PARI) vector(40, n, n--; (14*6^n-(-7)^n)/13) \\ _G. C. Greubel_, Oct 20 2018

%o (Magma) [(14*6^n-(-7)^n)/13: n in [0..40]]; // _G. C. Greubel_, Oct 20 2018

%K easy,sign

%O 0,2

%A _Philippe Deléham_, Sep 21 2009