This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A255116 #21 Feb 20 2023 16:44:49
%S A255116 1,3,10,33,108,354,1161,3807,12483,40932,134217,440100,1443096,
%T A255116 4731939,15516117,50877639,166828734,547034553,1793736576,5881695930,
%U A255116 19286191449,63239784075,207364440015,679951894392,2229575035401,7310818426248,23972310961920
%N A255116 Number of n-length words on {0,1,2,3} in which 0 appears only in runs of length 2.
%H A255116 Colin Barker, <a href="/A255116/b255116.txt">Table of n, a(n) for n = 0..1000</a>
%H A255116 D. Birmajer, J. B. Gil, and M. D. Weiner, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Gil/gil6.html">On the Enumeration of Restricted Words over a Finite Alphabet</a>, J. Int. Seq. 19 (2016) # 16.1.3, example 10.
%H A255116 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,3).
%F A255116 a(n+3) = 3*a(n+2) + 3*a(n) with n>1, a(0) = 1, a(1) = 3, a(2) = 10.
%F A255116 G.f.: -(x^2+1) / (3*x^3+3*x-1). - _Colin Barker_, Feb 15 2015
%F A255116 a(n) = A089978(n) + A089978(n-2). - _R. J. Mathar_, Aug 04 2019
%t A255116 RecurrenceTable[{a[0] == 1, a[1] == 3, a[2]== 10, a[n] == 3 a[n - 1] + 3 a[n - 3]}, a[n], {n, 0, 25}]
%t A255116 LinearRecurrence[{3,0,3},{1,3,10},30] (* _Harvey P. Dale_, Feb 20 2023 *)
%o A255116 (PARI) Vec(-(x^2+1)/(3*x^3+3*x-1) + O(x^100)) \\ _Colin Barker_, Feb 15 2015
%Y A255116 Cf. A000930, A239333, A239340, A254657, A254600, A254664.
%K A255116 nonn,easy
%O A255116 0,2
%A A255116 _Milan Janjic_, Feb 14 2015