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Number of ascending runs in {1,...,7}^n.
2

%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