A189612
Number of n X 4 binary arrays without the pattern 0 1 0 diagonally, antidiagonally or horizontally.
Original entry on oeis.org
12, 144, 1164, 8496, 65160, 515560, 4075336, 32031600, 251533888, 1976926440, 15543816656, 122208548968, 960755182696, 7553047614920, 59379727197728, 466827426445200, 3670067881137352, 28853031765433504, 226834374728410104
Offset: 1
Some solutions for 3 X 4
..1..1..1..1....0..1..1..0....1..1..0..0....1..0..0..0....1..1..1..0
..1..1..0..1....1..1..0..1....1..1..1..0....1..0..1..1....0..1..1..0
..0..0..1..1....1..0..1..1....1..1..1..0....1..1..0..1....0..1..1..1
A189613
Number of nX5 binary arrays without the pattern 0 1 0 diagonally, antidiagonally or horizontally.
Original entry on oeis.org
21, 441, 5238, 50024, 532565, 6110500, 69943253, 783072552, 8759983583, 98440457351, 1108879339651, 12480666817260, 140421583259356, 1580016922218493, 17782853849081975, 200149452833682454
Offset: 1
Some solutions for 3X5
..0..1..1..0..0....0..1..1..0..1....1..1..0..1..1....0..0..0..0..1
..1..0..0..1..1....1..1..1..1..0....1..0..0..1..1....0..0..0..1..1
..1..1..1..0..0....0..1..1..0..1....1..1..0..1..1....1..1..0..0..1
A189614
Number of nX6 binary arrays without the pattern 0 1 0 diagonally, antidiagonally or horizontally.
Original entry on oeis.org
37, 1369, 25046, 357323, 6204967, 118571483, 2239578131, 41236726541, 764615054191, 14279876468131, 267312630925466, 4997721311916752, 93457924722647556, 1748307417599408282, 32716532907276172258
Offset: 1
Some solutions for 3X6
..1..1..1..0..0..1....0..1..1..1..0..1....1..1..1..1..0..0....0..1..1..1..1..0
..1..1..1..1..0..1....1..0..0..1..1..1....0..1..1..0..0..1....0..0..1..1..1..1
..0..1..1..1..0..1....1..1..1..1..0..0....1..0..1..1..1..0....1..1..1..1..1..1
A189615
Number of nX7 binary arrays without the pattern 0 1 0 diagonally, antidiagonally or horizontally.
Original entry on oeis.org
65, 4225, 116100, 2482591, 68121839, 2076231513, 61652076124, 1785011303305, 52081392909734, 1531637258052071, 45087524679984918, 1325492265359151122, 38967877720497094747, 1146070566293713302197, 33712980614275859943483
Offset: 1
Some solutions for 3X7
..0..0..1..1..1..0..1....0..0..1..1..0..1..1....1..1..1..1..0..0..1
..1..0..1..1..0..0..0....0..0..0..0..0..0..1....1..0..1..1..0..0..0
..1..1..0..1..1..1..0....1..0..1..1..1..1..0....1..0..1..1..1..1..1
A189616
Number of nX8 binary arrays without the pattern 0 1 0 diagonally, antidiagonally or horizontally.
Original entry on oeis.org
114, 12996, 526418, 15915001, 636683482, 28823835852, 1256763617551, 52939317116118, 2243913970341972, 96114581661833896, 4121472431976051699, 176378174243580691358, 7545272457917436835785, 322957852724963531996423
Offset: 1
Some solutions for 3X8
..0..0..0..0..0..1..1..0....0..0..1..1..1..0..0..0....0..0..0..0..1..1..1..1
..0..0..0..0..1..1..0..1....1..0..1..1..0..0..0..1....1..1..0..0..1..1..0..1
..0..1..1..0..0..1..1..1....0..0..1..1..0..0..1..1....1..1..1..1..0..1..1..0
A189618
Number of 3Xn binary arrays without the pattern 0 1 0 diagonally, antidiagonally or horizontally.
Original entry on oeis.org
8, 64, 292, 1164, 5238, 25046, 116100, 526418, 2403976, 11065442, 50854642, 233077382, 1068505272, 4902990456, 22498260976, 103204910914, 473409837692, 2171794653270, 9963444579674, 45707359388096, 209680588779494
Offset: 1
Some solutions for 3X3
..0..0..1....0..1..1....1..0..1....0..0..1....1..1..0....0..1..1....1..1..0
..0..0..0....0..0..0....0..1..1....1..1..0....1..0..0....1..0..1....0..0..0
..0..1..1....1..0..1....0..1..1....0..0..1....1..1..1....0..0..0....1..1..0
A189619
Number of 4 X n binary arrays without the pattern 0 1 0 diagonally, antidiagonally or horizontally.
Original entry on oeis.org
16, 256, 1723, 8496, 50024, 357323, 2482591, 15915001, 100745265, 655633882, 4322765564, 28292943180, 183873191611, 1195974189947, 7802581300173, 50931021729006, 332106212299242, 2164490825527781, 14110729853099870
Offset: 1
Some solutions for 4 X 3:
1 1 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 0 1
1 0 1 1 0 0 0 0 1 1 0 1 1 0 1 1 0 1 0 1 1
1 1 1 1 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 1
0 1 1 1 1 0 1 1 1 0 1 1 1 0 0 1 1 0 1 0 1
-
Configs:= [seq(convert(n,base,2)[1..8],n=2^8..2^9-1)]:
Compatible:= proc(i,j) local Xi,Xj,k;
Xi:= Configs[i]; Xj:= Configs[j];
if Xi[5..8] <> Xj[1..4] then return 0 fi;
if Xi[1]=0 and ((Xi[5]=1 and Xj[5]=0) or (Xi[6]=1 and Xj[7]=0)) then return 0 fi;
if Xi[2]=0 and ((Xi[6]=1 and Xj[6]=0) or (Xi[7]=1 and Xj[8]=0)) then return 0 fi;
if Xi[3]=0 and ((Xi[6]=1 and Xj[5]=0) or (Xi[7]=1 and Xj[7]=0)) then return 0 fi;
if Xi[4]=0 and ((Xi[7]=1 and Xj[6]=0) or (Xi[8]=1 and Xj[8]=0)) then return 0 fi;
1
end proc:
T:= Matrix(256,256,Compatible):
Tu[0]:= u:
for nn from 1 to 30 do Tu[nn]:= T . Tu[nn-1] od:
[16, seq(u^%T . Tu[n],n=0..30)]; # Robert Israel, Oct 20 2019
A189620
Number of 5 X n binary arrays without the pattern 0 1 0 diagonally, antidiagonally or horizontally.
Original entry on oeis.org
32, 1024, 10327, 65160, 532565, 6204967, 68121839, 636683482, 5785616468, 56137313726, 563010113815, 5529846867761, 53193183705288, 513158091226513, 5003028394342619, 48867656731556592, 475282571037202342
Offset: 1
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
-
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
A189621
Number of 6 X n binary arrays without the pattern 0 1 0 diagonally, antidiagonally or horizontally.
Original entry on oeis.org
64, 4096, 61996, 515560, 6110500, 118571483, 2076231513, 28823835852, 385459961106, 5723963509791, 89346030665338, 1342965562065607, 19505273464622126, 285343732611331021, 4255443558501922341
Offset: 1
Some solutions for 6 X 3
..0..0..0....1..0..1....1..0..1....1..1..1....1..1..0....0..0..1....1..0..1
..1..0..1....0..1..1....1..0..0....1..0..0....1..1..1....1..0..1....1..1..1
..1..1..1....1..0..0....0..0..0....1..0..0....1..0..1....0..0..0....1..1..1
..0..1..1....0..0..1....1..0..0....1..1..1....1..1..0....0..0..1....1..1..0
..1..0..1....0..0..1....0..0..0....1..0..0....1..1..1....0..0..1....0..0..0
..1..1..0....1..0..1....1..1..1....1..0..1....1..1..0....0..0..1....1..0..1
A189622
Number of 7Xn binary arrays without the pattern 0 1 0 diagonally, antidiagonally or horizontally.
Original entry on oeis.org
128, 16384, 371641, 4075336, 69943253, 2239578131, 61652076124, 1256763617551, 24523253340435, 553063756559791, 13299838117765230, 302455226663091586, 6562256770141965765, 144156209612197100001, 3257064388881887530527
Offset: 1
Some solutions for 7X3
..0..0..1....0..0..0....0..0..1....0..0..0....0..0..1....0..0..1....0..0..1
..1..1..1....0..0..1....1..1..0....1..0..1....1..0..0....1..0..1....1..1..1
..1..0..1....0..0..1....1..1..1....1..1..1....1..0..0....1..0..1....1..1..1
..1..0..1....1..0..1....1..0..1....0..1..1....1..1..1....1..0..1....1..1..0
..1..1..1....1..1..0....1..0..1....0..1..1....1..1..1....0..0..0....0..0..0
..0..1..1....0..0..0....0..0..1....1..0..1....0..1..1....0..0..0....0..0..1
..1..1..0....1..0..1....1..0..1....1..1..1....1..0..0....1..1..0....1..1..1
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