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A255631 Number of n-length words on {0,1,2,3} avoiding runs of zeros of length 1 (mod 3).

%I A255631 #21 Aug 01 2021 15:09:18
%S A255631 1,3,10,34,114,382,1282,4302,14434,48430,162498,545230,1829410,
%T A255631 6138222,20595586,69104398,231866082,777980590,2610359362,8758542414,
%U A255631 29387549602,98604086254,330846428418,1110089483662,3724684796002,12497440101678,41932678239682
%N A255631 Number of n-length words on {0,1,2,3} avoiding runs of zeros of length 1 (mod 3).
%H A255631 Colin Barker, <a href="/A255631/b255631.txt">Table of n, a(n) for n = 0..1000</a>
%H A255631 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,4).
%F A255631 a(n+3) = 3*a(n+2) + 4*a(n) with n > 0, a(0) = 1, a(1) = 3, a(2) = 10.
%F A255631 G.f.: -(x^2+1) / (4*x^3+3*x-1). - _Colin Barker_, Mar 20 2015
%t A255631 RecurrenceTable[{a[0] == 1, a[1] == 3,  a[2] == 10,  a[n] == 3* a[n - 1] +  4*a[n - 3]}, a[n], {n, 0, 25}]
%t A255631 LinearRecurrence[{3,0,4},{1,3,10},40] (* _Harvey P. Dale_, Aug 01 2021 *)
%Y A255631 Cf. A254598, A254602, A255115, A255117, A254601, A254663.
%K A255631 nonn,easy
%O A255631 0,2
%A A255631 _Milan Janjic_, Feb 28 2015