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