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Number of ascending runs in {1,...,9}^n.
2

%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