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%I #10 Oct 26 2016 11:08:33
%S 1,4,13,42,136,440,1423,4602,14883,48132,155660,503408,1628033,
%T 5265096,17027441,55067134,178088372,575941872,1862609199,6023720790,
%U 19480850935,63001517896,203748351160,658926832032,2130984459505,6891652526348,22287762039781
%N Number of n-length words over a quaternary alphabet {a_1,a_2,...,a_4} avoiding consecutive letters a_i, a_{i+1}.
%H Alois P. Heinz, <a href="/A277667/b277667.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3,2,-1)
%F G.f.: 1/(1 + Sum_{j=1..4} (5-j)*(-x)^j).
%e a(3) = 42: 000, 002, 003, 020, 021, 022, 030, 031, 032, 033, 100, 102, 103, 110, 111, 113, 130, 131, 132, 133, 200, 202, 203, 210, 211, 213, 220, 221, 222, 300, 302, 303, 310, 311, 313, 320, 321, 322, 330, 331, 332, 333 (using alphabet {0, 1, 2, 3}).
%p a:= n-> (<<0|1|0|0>, <0|0|1|0>, <0|0|0|1>, <-1|2|-3|4>>^n)[4, 4]:
%p seq(a(n), n=0..30);
%Y Column k=4 of A277666.
%K nonn,easy
%O 0,2
%A _Alois P. Heinz_, Oct 26 2016
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