%I #13 Dec 21 2018 18:06:23

%S 188,404,836,1700,3428,6884,13796,27620,55268,110564,221156,442340,

%T 884708,1769444,3538916,7077860,14155748,28311524,56623076,113246180,

%U 226492388,452984804,905969636,1811939300,3623878628,7247757284

%N Number of 4 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) = 27*2^n-28.

%o (PARI) vector(50, n, i=n+2; 27*2^i-28) \\ _Michel Marcus_, Dec 01 2014

%Y Cf. A000105.

%K nonn

%O 3,1

%A _Sergey Kitaev_, Nov 12 2004