%I #12 May 24 2024 15:53:28
%S 0,9,126,1539,17496,190269,2007666,20726199,210450636,2109289329,
%T 20920706406,205720279659,2008387814976,19487638017189,
%U 188098071296346,1807266603941919,17294855095950516,164918796807813849,1567655079768657486,14859368894402912979
%N Number of ascending runs in {1,...,9}^n.
%H Alois P. Heinz, <a href="/A229283/b229283.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (18,-81).
%F G.f.: -9*(4*x-1)*x/(9*x-1)^2.
%F a(n) = 9^(n-1)*(5*n+4) for n>0, a(0) = 0.
%F a(n) = 18*a(n-1) - 81*a(n-2). - _Wesley Ivan Hurt_, May 24 2024
%p a:= n-> `if`(n=0, 0, 9^(n-1)*(5*n+4)):
%p seq(a(n), n=0..30);
%Y Column k=9 of A229079.
%K nonn,easy
%O 0,2
%A _Alois P. Heinz_, Sep 18 2013