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A099943 Number of 5 X n binary matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01,1) and (11;0).

%I A099943 #21 Jul 04 2025 19:21:54
%S A099943 72,98,124,150,176,202,228,254,280,306,332,358,384,410,436,462,488,
%T A099943 514,540,566,592,618,644,670,696,722,748,774,800,826,852,878,904,930,
%U A099943 956,982,1008,1034,1060,1086,1112,1138,1164,1190,1216,1242,1268,1294,1320
%N A099943 Number of 5 X n binary matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01,1) and (11;0).
%C A099943 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 (n+2)*2^(m-1)+2*m*(n-1)-2 for m>1 and n>1.
%H A099943 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H A099943 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 A099943 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A099943 a(n) = 26*n + 20.
%F A099943 From _Elmo R. Oliveira_, Jul 01 2025: (Start)
%F A099943 G.f.: 2*x^2*(36-23*x)/(1-x)^2.
%F A099943 E.g.f.: 2*(exp(x)*(10 + 13*x) - (10 + 23*x)).
%F A099943 a(n) = 2*a(n-1) - a(n-2) for n > 3.
%F A099943 a(n) = A252994(n) + 20. (End)
%t A099943 Range[72, 7000, 26] (* _Vladimir Joseph Stephan Orlovsky_, Jul 13 2011 *)
%Y A099943 Cf. A016957 (m=2), A008592 (m=3), A063130 (m=4).
%Y A099943 Cf. A252994.
%K A099943 nonn,easy
%O A099943 2,1
%A A099943 _Sergey Kitaev_, Nov 12 2004