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 A084478 #32 Dec 08 2022 11:36:39
%S A084478 1,0,72,384,8544,76800,1168512,12785664,170678784,2014648320,
%T A084478 25633231872,311423852544,3892030055424,47803588208640,
%U A084478 593425578949632,7318730222874624,90624271197041664,1119402280975349760,13847850677651745792,171150049715628539904
%N A084478 Number of tilings of a 5 X 3n rectangle with right trominoes.
%C A084478 A right tromino is a 3-celled L-shaped piece (a 2 X 2 square with one of the four cells omitted). - _N. J. A. Sloane_, Mar 28 2017
%C A084478 There is a sign typo with respect to the g.f. in the paper.
%C A084478 The sequence is the Hadamard sum of the following 4 sequences: 0, 0, 0, 0, 2048, 0, 65536, 0,.. (tilings which have both vertical and horizontal faults), 0, 0, 64, 0, 0, 0, 0, 0.. (tilings which have horizontal but no vertical faults), 0, 0, 0, 0, 3136, 55296, 939008, 11649024... (tilings which have vertical faults but no horizontal faults), .. 1, 0, 8, 384, 3360, 21504, 163968 (essentially A084479) which have neither vertical nor horizontal faults. - _R. J. Mathar_, Dec 08 2022
%H A084478 Colin Barker, <a href="/A084478/b084478.txt">Table of n, a(n) for n = 0..900</a>
%H A084478 D. Merlini, R. Sprugnoli, M. C. Verri, <a href="https://doi.org/10.1016/S0304-3975(98)00204-7">Strip tiling and regular grammars</a>, Theo. Comp. Sci. 242 (1-2) (2000) 109-124, Proof of Theorem 4.2 (typo t^5 in the denominator of g.f. ought be t^6)
%H A084478 C. Moore, <a href="https://arxiv.org/abs/math/9905012">Some Polyomino Tilings of the Plane</a>, arXiv:math/9905012 [math.CO], 1999.
%H A084478 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,103,280,380).
%F A084478 G.f.: (1 - 2*z - 31*z^2 - 40*z^3 - 20*z^4) / (1 - 2*z - 103*z^2 - 280*z^3 - 380*z^4).
%F A084478 a(n) = 2*a(n-1) + 103*a(n-2) + 280*a(n-3) + 380*a(n-4) for n > 4. - _Colin Barker_, Mar 27 2017
%t A084478 LinearRecurrence[{2, 103, 280, 380}, {72, 384, 8544, 76800}, 20] (* _Jean-François Alcover_, Jan 07 2019 *)
%o A084478 (PARI) Vec(24*x^2*(3 + 10*x + 15*x^2) / (1 - 2*x - 103*x^2 - 280*x^3 - 380*x^4) + O(x^30)) \\ _Colin Barker_, Mar 27 2017
%Y A084478 Cf. A046984, A084477, A084479 (INVERT transform), A084480, A084481,A351323, A351324, A236576 (straight trominoes), A233340 (mixed trominoes).
%K A084478 nonn,easy
%O A084478 0,3
%A A084478 _Ralf Stephan_, May 27 2003
%E A084478 a(0) and a(1) prepended by _Alois P. Heinz_, Feb 21 2022