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 A178869 a(n) = 9*a(n-1) - 10*a(n-2); a(0)=0, a(1)=1. 4

%I

%S 0,1,9,71,549,4231,32589,250991,1933029,14887351,114655869,883029311,

%T 6800705109,52376052871,403377424749,3106636294031,23925952398789,

%U 184267208648791,1419145353851229,10929636098173151,84175271345046069

%N a(n) = 9*a(n-1) - 10*a(n-2); a(0)=0, a(1)=1.

%C Alternating row sums of triangle A206819. Large Schroeder numbers in decimal expansion of ratio a(n)/a(n+1). [A-number corrected by _Philippe Deléham_, Feb 26 2013]

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (9, -10).

%F G.f.: -x/(-10*x^2+9*x-1).

%F a(n) = 9a(n-1)-10a(n-2), a(0)=0, a(1)=1. [_Harvey P. Dale_, May 06 2011]

%F a(n) = 1/sqrt(41)*((9/2+1/2*sqrt(41))^n-(9/2-1/2*sqrt(41))^n). - _Paolo P. Lava_, Jun 06 2011

%F a(n+1) = Sum_{k, 0<=k<=n}A206819(n,k)*(-1)^k. - _Philippe Deléham_, Feb 26 2013

%t Join[{a=0,b=1},Table[c=9*b-10*a+2;a=b;b=c,{n,60}]] (* _Vladimir Joseph Stephan Orlovsky_, Jan 20 2011 *)

%t LinearRecurrence[{9,-10},{0,1},50] (* or *) CoefficientList[Series[ -x/(-10x^2+9x-1),{x,0,50}],x] (* _Harvey P. Dale_, May 06 2011 *)

%Y Cf. A006318, A171415, A104562, A206819.

%K nonn,easy

%O 0,3

%A _Mark Dols_, Jun 20 2010

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Last modified March 26 23:01 EDT 2019. Contains 321565 sequences. (Running on oeis4.)