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a(0)=1, a(1)=9, a(n) = 72*a(n-2) - a(n-1).
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%I #19 Sep 08 2022 08:45:47

%S 1,9,63,585,3951,38169,246303,2501865,15231951,164902329,931798143,

%T 10941169545,56148296751,731615910489,3311061455583,49365284099625,

%U 189031140702351,3365269314470649,10244972816098623,232054417825788105

%N a(0)=1, a(1)=9, a(n) = 72*a(n-2) - a(n-1).

%C a(n)/a(n-1) tends to -9.

%C First term < 0: a(27) = -60053864762402471338497.

%H Harvey P. Dale, <a href="/A165510/b165510.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, 72).

%F G.f.: (1+10*x)/(1+x-72*x^2).

%F a(n) = Sum_{k=0..n} A112555(n,k)*8^k.

%F a(n) = (18*8^n-(-9)^n)/17. - _Klaus Brockhaus_, Sep 26 2009

%F E.g.f.: (18*exp(8*x) - exp(-9*x))/17. - _G. C. Greubel_, Oct 21 2018

%t LinearRecurrence[{-1,72},{1,9},30] (* _Harvey P. Dale_, Oct 15 2012 *)

%o (PARI) vector(30, n, n--; (18*8^n-(-9)^n)/17) \\ _G. C. Greubel_, Oct 21 2018

%o (Magma) [(18*8^n-(-9)^n)/17: n in [0..30]]; // _G. C. Greubel_, Oct 21 2018

%K sign

%O 0,2

%A _Philippe Deléham_, Sep 21 2009