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A189620 Number of 5 X n binary arrays without the pattern 0 1 0 diagonally, antidiagonally or horizontally.

%I A189620 #14 Oct 23 2019 03:21:21
%S A189620 32,1024,10327,65160,532565,6204967,68121839,636683482,5785616468,
%T A189620 56137313726,563010113815,5529846867761,53193183705288,
%U A189620 513158091226513,5003028394342619,48867656731556592,475282571037202342
%N A189620 Number of 5 X n binary arrays without the pattern 0 1 0 diagonally, antidiagonally or horizontally.
%C A189620 Row 5 of A189617.
%H A189620 R. H. Hardin, <a href="/A189620/b189620.txt">Table of n, a(n) for n = 1..200</a>
%H A189620 Robert Israel, <a href="/A189620/a189620.txt">Linear recurrence of order 147</a>
%H A189620 Robert Israel, <a href="/A189620/a189620.pdf">Maple-assisted derivation of recurrence</a>
%F A189620 Linear recurrence of order 147 (see links). - _Robert Israel_, Oct 22 2019
%e A189620 Some solutions for 5 X 3:
%e A189620   0 0 0   0 0 0   1 0 1   0 0 0   0 1 1   0 1 1   0 0 0
%e A189620   1 0 1   0 1 1   1 1 1   0 0 1   0 0 1   0 0 0   0 0 0
%e A189620   0 0 1   1 1 1   1 1 1   0 0 0   1 0 0   0 0 1   0 0 1
%e A189620   1 1 0   0 0 1   1 0 0   1 0 1   1 0 0   0 0 1   1 0 0
%e A189620   0 0 1   0 0 1   0 0 0   1 1 1   0 0 1   1 0 0   0 1 1
%p A189620 Compatible:= proc(i,j) local Xi,Xj,k;
%p A189620 Xi:= Configs[i]; Xj:= Configs[j];
%p A189620 if Xi[6..10] <> Xj[1..5] then return 0 fi;
%p A189620 if Xi[1]=0 and ((Xi[6]=1 and Xj[6]=0) or (Xi[7]=1 and Xj[8]=0)) then return 0 fi;
%p A189620 if Xi[2]=0 and ((Xi[7]=1 and Xj[7]=0) or (Xi[8]=1 and Xj[9]=0)) then return 0 fi;
%p A189620 if Xi[3]=0 and ((Xi[7]=1 and Xj[6]=0) or (Xi[8]=1 and Xj[8]=0) or (Xi[9]=1 and Xj[10]=0)) then return 0 fi;
%p A189620 if Xi[4]=0 and ((Xi[8]=1 and Xj[7]=0) or (Xi[9]=1 and Xj[9]=0)) then return 0 fi;
%p A189620 if Xi[5]=0 and ((Xi[9]=1 and Xj[8]=0) or (Xi[10]=1 and Xj[10]=0)) then return 0 fi;
%p A189620 1
%p A189620 end proc:
%p A189620 T:= Matrix(1024,1024,Compatible):
%p A189620 u:= Vector(1024,1):
%p A189620 Tu[0]:= u:
%p A189620 for nn from 1 to 30 do Tu[nn]:= T . Tu[nn-1] od:
%p A189620 32, seq(u^%T . Tu[n],n=0..30); # _Robert Israel_, Oct 22 2019
%K A189620 nonn
%O A189620 1,1
%A A189620 _R. H. Hardin_, Apr 24 2011