Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #36 Dec 18 2023 12:20:48
%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) = 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