%I #15 Dec 18 2025 15:30:25

%S 0,10,155,2100,26500,320000,3750000,43000000,485000000,5400000000,

%T 59500000000,650000000000,7050000000000,76000000000000,

%U 815000000000000,8700000000000000,92500000000000000,980000000000000000,10350000000000000000,109000000000000000000

%N Number of ascending runs in {1,...,10}^n.

%H Alois P. Heinz, <a href="/A229284/b229284.txt">Table of n, a(n) for n = 0..990</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20,-100).

%F G.f.: -5*(9*x-2)*x/(10*x-1)^2.

%F a(n) = 10^(n-1)*(11*n+9)/2 for n>0, a(0) = 0.

%F From _Elmo R. Oliveira_, Nov 20 2025: (Start)

%F E.g.f.: (exp(10*x)*(110*x + 9) - 9)/20.

%F a(n) = 20*a(n-1) - 100*a(n-2) for n > 2. (End)

%p a:= n-> `if`(n=0, 0, 10^(n-1)*(11*n+9)/2):

%p seq(a(n), n=0..30);

%t LinearRecurrence[{20,-100},{0,10,155},20] (* _Harvey P. Dale_, Dec 18 2025 *)

%Y Column k=10 of A229079.

%K nonn,easy

%O 0,2

%A _Alois P. Heinz_, Sep 18 2013