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 A046984 #35 Mar 14 2023 11:09:56
%S A046984 1,4,18,88,468,2672,16072,100064,636368,4097984,26579488,173093760,
%T A046984 1129796928,7383588608,48287978624,315921649152,2067346607360,
%U A046984 13530037877760,88555066819072,579620448450560,3793872862974976,24832858496561152,162544900186359808
%N A046984 Number of ways to tile a 4 X 3n rectangle with right trominoes.
%C A046984 The sequence of tiling 2 X 3n rectangles with L-trominoes is 2^n. The sequence of tiling 3 X 2n rectangles is 2^n. All these tilings have vertical faults but no horizontal faults. - _R. J. Mathar_, Dec 08 2022
%C A046984 This sequence is the Hadamard sum of the following 4 sequences: 0, 0, 16, 64, 256, 1024, 4096... (A000302, tilings which have both vertical and horizontal faults), 0, 4, 0, 0, 0, 0, 0, ...(tilings which have horizontal but no vertical faults), 0, 0, 0, 16, 164, 1360, 10248, 73312, 508624, 3462592, 23291424.. (tilings which have vertical but no horizontal faults), 1, 0, 2, 8, 48, 288, 1728, 10368,.. (essentially A084477, tilings which have neither vertical nor horizontal faults). - _R. J. Mathar_, Dec 08 2022
%D A046984 Suggested on p. 96 of 1994 edition of "Polyominoes" by Samuel W. Golomb.
%H A046984 R. J. Mathar, <a href="/A046984/a046984.pdf">Fault-free tilings with dominoes or trominoes.</a>
%H A046984 Cristopher Moore, <a href="http://www.santafe.edu/~moore">Preprint and figures</a>
%H A046984 Cristopher Moore, <a href="https://arxiv.org/abs/math/9905012">Some Polyomino Tilings of the Plane</a>, arXiv:math/9905012 [math.CO], 1999.
%H A046984 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (10,-22,-4).
%F A046984 G.f.: (1 - 6*x)/(1 - 10*x + 22*x^2 + 4*x^3).
%F A046984 a(0)=1, a(1)=4, a(2)=18, a(n)=10*a(n-1)-22*a(n-2)-4*a(n-3). - _Harvey P. Dale_, Mar 31 2012
%p A046984 a:= n-> (<<0|1|0>, <0|0|1>, <-4|-22|10>>^n. <<1, 4, 18>>)[1, 1]:
%p A046984 seq(a(n), n=0..22); # _Alois P. Heinz_, Feb 21 2022
%t A046984 CoefficientList[Series[(1-6x)/(1-10x+22x^2+4x^3),{x,0,40}],x] (* or *) LinearRecurrence[{10,-22,-4},{1,4,18},40] (* _Harvey P. Dale_, Mar 31 2012 *)
%o A046984 (PARI) a(n)=([0,1,0; 0,0,1; -4,-22,10]^n*[1;4;18])[1,1] \\ _Charles R Greathouse IV_, Feb 10 2017
%Y A046984 Cf. A084478 (5 X 3n), A351323 (6 X n), A351324 (7 X 3n), A049086 (straight trominoes), A233339 (mixed trominoes).
%K A046984 nonn,easy,nice
%O A046984 0,2
%A A046984 Cristopher Moore (moore(AT)santafe.edu)