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 A099041 #19 Jun 18 2025 13:48:34
%S A099041 1,8,24,58,128,270,556,1130,2280,4582,9188,18402,36832,73694,147420,
%T A099041 294874,589784,1179606,2359252,4718546,9437136,18874318,37748684,
%U A099041 75497418,150994888,301989830,603979716,1207959490,2415919040,4831838142,9663676348,19327352762
%N A099041 Number of 3 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (10;0) and (10;1).
%C A099041 An occurrence of a ranpp (xy;z) in a matrix A=(a(i,j)) is a triple (a(i1,j1), a(i1,j2), a(i2,j1)) where i1<i2, j1<j2 and these elements are in the same relative order as those in the triple (x,y,z). In general, the number of m X n 0-1 matrices in question is given by g.f. 2xy/((1-2x)(1-(2-x)y/(1-x))).
%H A099041 S. Kitaev, <a href="http://www.emis.de/journals/INTEGERS/papers/e21/e21.Abstract.html">On multi-avoidance of right angled numbered polyomino patterns</a>, Integers: Electronic Journal of Combinatorial Number Theory 4 (2004), A21, 20pp.
%H A099041 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4, -5, 2).
%F A099041 G.f.: 1 + 2*x*(2-x)^2/((1-2*x)*(1-x)^2).
%F A099041 a(n) = 9*2^n - 2*n - 8.
%F A099041 a(n) = 2 * (A054127(n+1) - 1) for n>0.
%t A099041 LinearRecurrence[{4,-5,2},{1,8,24},40] (* _Harvey P. Dale_, Jun 18 2025 *)
%o A099041 (PARI) vector(50, n, 9*2^n - 2*n - 8) \\ _Michel Marcus_, Dec 01 2014
%Y A099041 Cf. A054127.
%K A099041 nonn,easy
%O A099041 0,2
%A A099041 _Sergey Kitaev_, Nov 13 2004
%E A099041 a(0)=1 prepended by _Alois P. Heinz_, Dec 21 2018