|
%I #16 Sep 08 2022 08:45:09
%S 1,19,262,3196,36568,402544,4320352,45562816,474502528,4896020224,
%T 50168161792,511345294336,5190762354688,52526098837504,
%U 530208790700032,5341670325600256,53733362604802048,539866900838416384
%N 9th binomial transform of the periodic sequence (1,10,1,1,10,1...).
%H Vincenzo Librandi, <a href="/A081036/b081036.txt">Table of n, a(n) for n = 0..300</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (18,-80).
%F a(n) = 10*a(n-1)+9*8^(n-1).
%F a(n) = (11/2)*10^n-(9/2)*8^n.
%F G.f.: (1+x)/((1-8*x)*(1-10*x)). - _Vincenzo Librandi_, Aug 06 2013
%F a(0)=1, a(1)=19, a(n)=18*a(n-1)-80*a(n-2). - _Harvey P. Dale_, Aug 16 2014
%t CoefficientList[Series[(1 + x)/((1 - 8 x) (1 - 10 x)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Aug 06 2013 *)
%t LinearRecurrence[{18,-80},{1,19},20] (* _Harvey P. Dale_, Aug 16 2014 *)
%o (Magma) [(11/2)*10^n-(9/2)*8^n: n in [0..25]]; // _Vincenzo Librandi_, Aug 06 2013
%Y Cf. A081034, A081035.
%K nonn,easy
%O 0,2
%A _Paul Barry_, Mar 03 2003
%E Corrected by _T. D. Noe_, Nov 07 2006
|
