%I #11 Jul 01 2023 15:59:57
%S 0,6,57,468,3564,25920,182736,1259712,8538048,57106944,377913600,
%T 2479113216,16144468992,104485552128,672625741824,4310029025280,
%U 27505821597696,174908814262272,1108696193630208,7007637010120704,44178581150760960,277868041444786176
%N Number of ascending runs in {1,...,6}^n.
%H Alois P. Heinz, <a href="/A229280/b229280.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 (12,-36).
%F G.f.: -3*(5*x-2)*x/(6*x-1)^2.
%F a(n) = 6^(n-1)*(7*n+5)/2 for n>0, a(0) = 0.
%p a:= n-> `if`(n=0, 0, 6^(n-1)*(7*n+5)/2):
%p seq(a(n), n=0..30);
%Y Column k=6 of A229079.
%K nonn,easy
%O 0,2
%A _Alois P. Heinz_, Sep 18 2013