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%I #21 Dec 21 2018 18:06:51
%S 76,164,340,692,1396,2804,5620,11252,22516,45044,90100,180212,360436,
%T 720884,1441780,2883572,5767156,11534324,23068660,46137332,92274676,
%U 184549364,369098740,738197492,1476394996,2952790004,5905580020
%N Number of 3 X n binary matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1) and (11;0).
%C 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 (m+3)*2^(m+n-2)-2^n-2^(m+1)+4 for m>0 and n>2; for n=2 the number is (m+1)*2^m.
%H 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 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F a(n) = 11*2^n - 12.
%F From _Chai Wah Wu_, Jun 06 2016: (Start)
%F a(n) = 3*a(n-1) - 2*a(n-2) for n > 4.
%F G.f.: 4*x^3*(19 - 16*x)/((1 - x)*(1 - 2*x)). (End)
%t LinearRecurrence[{3,-2},{76,164},30] (* _Harvey P. Dale_, Oct 22 2017 *)
%o (PARI) vector(50, n, i=n+2; 11*2^i - 12) \\ _Michel Marcus_, Dec 01 2014
%Y Cf. A000105.
%K nonn,easy
%O 3,1
%A _Sergey Kitaev_, Nov 12 2004