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Number of 0..3 arrays of length n avoiding the consecutive pattern 0..3.
4

%I #13 Jun 30 2021 12:31:59

%S 4,16,64,255,1016,4048,16128,64257,256012,1020000,4063872,16191231,

%T 64508912,257015648,1023998720,4079803649,16254705684,64761807088,

%U 258023229632,1028013114879,4095797753832,16318429208240,65015693603328

%N Number of 0..3 arrays of length n avoiding the consecutive pattern 0..3.

%C Column 3 of A206455.

%H R. H. Hardin, <a href="/A206450/b206450.txt">Table of n, a(n) for n = 1..210</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,0,0,-1).

%F a(n) = 4*a(n-1) -a(n-4).

%F Empirical: a(n) = sum{i in 0..floor(n/4)} ((-1)^i*4^(n-4*i)*binomial(n-3*i,i)).

%F g.f.: x*(4 - x^3) / (1 - 4*x + x^4). - _Colin Barker_, Feb 23 2018

%Y Cf. A206455.

%K nonn,easy

%O 1,1

%A _R. H. Hardin_, Feb 07 2012