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A206453 Number of 0..6 arrays of length n avoiding the consecutive pattern 0..6. 1


%S 7,49,343,2401,16807,117649,823542,5764787,40353460,282473877,

%T 1977314738,13841186359,96888186864,678216484506,4747509626755,

%U 33232527033825,232627406762898,1628389870025548,11398715248992477,79790909854760475

%N Number of 0..6 arrays of length n avoiding the consecutive pattern 0..6.

%C Column 6 of A206455.

%H R. H. Hardin, <a href="/A206453/b206453.txt">Table of n, a(n) for n = 1..210</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,0,0,0,0,0,-1).

%F a(n) = 7*a(n-1) - a(n-7).

%F Empirical: a(n) = Sum_{i=0..floor(n/7)} ((-1)^i*7^(n-7*i)*binomial(n-6*i,i)).

%F g.f.: x*(7 - x^6) / (1 - 7*x + x^7). - _Colin Barker_, Jun 16 2018

%Y Cf. A206455.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 07 2012

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Last modified December 9 08:41 EST 2021. Contains 349627 sequences. (Running on oeis4.)