|
%I #15 Jan 03 2024 08:47:25
%S 1,1,19,280,4510,70300,1108900,17416000,273961000,4307050000,
%T 67726990000,1064904400000,16744473100000,263286127000000,
%U 4139863849000000,65094389920000000,1023531645610000000
%N a(n) = 10*a(n-1) + 90*a(n-2), n>2 ; a(0)=1, a(1)=1, a(2)=19 .
%C 10^(floor((n - 2)/2)) | a(n) for n>=1. - _G. C. Greubel_, Dec 30 2017
%H G. C. Greubel, <a href="/A155017/b155017.txt">Table of n, a(n) for n = 0..825</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10, 90).
%F G.f.: (1-9*x-81*x^2)/(1-10*x-90*x^2).
%F a(n+1) = Sum_{k=0..n} A154929(n,k)*9^(n-k).
%t Join[{1},LinearRecurrence[{10,90},{1,19},20]] (* _Harvey P. Dale_, Oct 10 2012 *)
%t CoefficientList[Series[(1 - 9*x - 81*x^2)/(1 - 10*x - 90*x^2), {x,0,50}], x] (* _G. C. Greubel_, Dec 30 2017 *)
%o (PARI) x='x+O('x^30); Vec((1-9*x-81*x^2)/(1-10*x-90*x^2)) \\ _G. C. Greubel_, Dec 30 2017
%o (Magma) I:=[1,1,19]; [1] cat [n le 2 select I[n] else 10*Self(n-1) + 90*Self(n-2): n in [1..30]]; // _G. C. Greubel_, Dec 30 2017
%K nonn
%O 0,3
%A _Philippe Deléham_, Jan 19 2009
|
