%I #11 Jul 01 2023 16:00:21
%S 0,7,77,735,6517,55223,453789,3647119,28824005,224827239,1735205101,
%T 13276336703,100843663893,761270796055,5716451614013,42728053589487,
%U 318086621166181,2359538070441671,17447288549040525,128644674234925471,946108300385970869
%N Number of ascending runs in {1,...,7}^n.
%H Alois P. Heinz, <a href="/A229281/b229281.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 (14,-49).
%F G.f.: -7*(3*x-1)*x/(7*x-1)^2.
%F a(n) = 7^(n-1)*(4*n+3) for n>0, a(0) = 0.
%p a:= n-> `if`(n=0, 0, 7^(n-1)*(4*n+3)):
%p seq(a(n), n=0..30);
%Y Column k=7 of A229079.
%K nonn,easy
%O 0,2
%A _Alois P. Heinz_, Sep 18 2013