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

32, 1024, 10327, 65160, 532565, 6204967, 68121839, 636683482, 5785616468, 56137313726, 563010113815, 5529846867761, 53193183705288, 513158091226513, 5003028394342619, 48867656731556592, 475282571037202342

Offset: 1

Author

R. H. Hardin, Apr 24 2011

Keywords

• nonn

Comments

Row 5 of A189617.

Examples

			Some solutions for 5 X 3:
  0 0 0   0 0 0   1 0 1   0 0 0   0 1 1   0 1 1   0 0 0
  1 0 1   0 1 1   1 1 1   0 0 1   0 0 1   0 0 0   0 0 0
  0 0 1   1 1 1   1 1 1   0 0 0   1 0 0   0 0 1   0 0 1
  1 1 0   0 0 1   1 0 0   1 0 1   1 0 0   0 0 1   1 0 0
  0 0 1   0 0 1   0 0 0   1 1 1   0 0 1   1 0 0   0 1 1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..200
• Robert Israel, Linear recurrence of order 147
• Robert Israel, Maple-assisted derivation of recurrence

Programs

Maple

Compatible:= proc(i,j) local Xi,Xj,k;
Xi:= Configs[i]; Xj:= Configs[j];
if Xi[6..10] <> Xj[1..5] then return 0 fi;
if Xi[1]=0 and ((Xi[6]=1 and Xj[6]=0) or (Xi[7]=1 and Xj[8]=0)) then return 0 fi;
if Xi[2]=0 and ((Xi[7]=1 and Xj[7]=0) or (Xi[8]=1 and Xj[9]=0)) then return 0 fi;
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;
if Xi[4]=0 and ((Xi[8]=1 and Xj[7]=0) or (Xi[9]=1 and Xj[9]=0)) then return 0 fi;
if Xi[5]=0 and ((Xi[9]=1 and Xj[8]=0) or (Xi[10]=1 and Xj[10]=0)) then return 0 fi;
1
end proc:
T:= Matrix(1024,1024,Compatible):
u:= Vector(1024,1):
Tu[0]:= u:
for nn from 1 to 30 do Tu[nn]:= T . Tu[nn-1] od:
32, seq(u^%T . Tu[n],n=0..30); # Robert Israel, Oct 22 2019

Formula

Linear recurrence of order 147 (see links). - Robert Israel, Oct 22 2019