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Number of ascending runs in {1,...,6}^n.
2

%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