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Number of 0..5 arrays of length n avoiding the consecutive pattern 0..5.
2

%I #14 Jun 30 2021 12:29:14

%S 6,36,216,1296,7776,46655,279924,1679508,10076832,60459696,362750400,

%T 2176455745,13058454546,78349047768,470084209776,2820444798960,

%U 16922306043360,101531659804415,609176900371944,3654983053183896

%N Number of 0..5 arrays of length n avoiding the consecutive pattern 0..5.

%C Column 5 of A206455.

%H R. H. Hardin, <a href="/A206452/b206452.txt">Table of n, a(n) for n = 1..210</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,0,0,0,0,-1).

%F a(n) = 6*a(n-1) - a(n-6).

%F Empirical: a(n) = Sum_{i=0..floor(n/6)} ((-1)^i*6^(n-6*i)*binomial(n-5*i,i)).

%F g.f.: x*(6 - x^5) / (1 - 6*x + x^6). - _Colin Barker_, Jun 16 2018

%Y Cf. A206455.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 07 2012