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a(0)=1, a(1)=10, a(n) = 90*a(n-2) - a(n-1).
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%I #21 Sep 08 2022 08:45:47

%S 1,10,80,820,6380,67420,506780,5561020,40049180,460442620,3143983580,

%T 38295852220,244662669980,3201964029820,18817676268380,

%U 269359086415420,1424231777738780,22818085999649020,105362773996841180

%N a(0)=1, a(1)=10, a(n) = 90*a(n-2) - a(n-1).

%C a(n)/a(n-1) tends to -10.

%C First entry < 0: a(30) = -8009307078719785774426912420.

%H G. C. Greubel, <a href="/A165511/b165511.txt">Table of n, a(n) for n = 0..998</a> (terms 0..100 from Franklin T. Adams-Watters)

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-1, 90).

%F G.f.: (1+11*x)/(1+x-90*x^2).

%F a(n) = Sum_{k=0..n} A112555(n,k)*9^k.

%F a(n) = (20*9^n-(-10)^n)/19. - _Klaus Brockhaus_, Sep 26 2009

%F E.g.f.: (20*exp(9*x) - exp(-10*x))/19. - _G. C. Greubel_, Oct 21 2018

%t LinearRecurrence[{-1,90},{1,10},20] (* or *) CoefficientList[Series[ (1+11x)/(1+x-90x^2),{x,0,20}],x] (* _Harvey P. Dale_, Apr 30 2011 *)

%o (PARI) vector(50, n, n--; (20*9^n-(-10)^n)/19) \\ _G. C. Greubel_, Oct 21 2018

%o (Magma) [(20*9^n-(-10)^n)/19: n in [0..50]]; // _G. C. Greubel_, Oct 21 2018

%K sign

%O 0,2

%A _Philippe Deléham_, Sep 21 2009