A295035
Number of nX3 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 2 1s.
Original entry on oeis.org
4, 29, 140, 741, 3853, 19956, 104096, 541775, 2819027, 14671776, 76356631, 397392690, 2068192977, 10763659993, 56018290276, 291541126302, 1517293977155, 7896590852333, 41096944195828, 213884557644749, 1113138825391146
Offset: 1
Some solutions for n=7
..1..1..0. .1..0..0. .0..0..0. .0..0..1. .0..1..0. .1..1..0. .0..0..0
..0..0..0. .1..0..0. .1..1..1. .1..0..1. .0..1..0. .1..0..1. .0..0..1
..1..1..0. .1..1..0. .0..0..1. .1..1..0. .0..1..0. .0..1..1. .0..1..1
..0..0..0. .0..0..1. .0..0..0. .0..0..0. .0..1..0. .0..1..0. .1..1..0
..0..0..0. .0..0..1. .1..1..0. .1..1..1. .1..0..1. .0..1..1. .1..0..1
..1..1..0. .1..1..0. .0..1..0. .0..0..0. .1..0..1. .1..0..1. .0..0..1
..1..0..0. .0..0..0. .0..0..0. .0..0..0. .1..1..1. .1..0..1. .0..0..1
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q:= proc(a,b) local r,s,t,M,i;
s:= floor((a-1)/8);
if s <> (b-1) mod 8 then return 0 fi;
s:= convert(s+8,base,2);
r:= convert(8+floor((b-1)/8),base,2);
t:= convert(8+ ((a-1) mod 8),base,2);
M:= Vector(3);
if s[1] = 1 and s[2] = 1 then M[1]:= 1; M[2]:= 1 fi;
if s[2]=1 and s[3]=1 then M[2]:= M[2]+1; M[3]:= 1 fi;
for i from 1 to 3 do if s[i]=1 then
M[i]:= M[i]+r[i]+t[i];
if M[i] = 0 or M[i]>2 then return 0 fi;
fi od;
1
end proc:
T:= Matrix(64,64, q);
u:= Vector[row](64):
v:= Vector(64):
for i from 0 to 7 do u[8*i+1]:= 1; v[i+1]:= 1;
od:
seq(u . T^n . v, n = 1 .. 100); # Robert Israel, Nov 12 2017
A295036
Number of nX4 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 2 1s.
Original entry on oeis.org
7, 87, 741, 6686, 59126, 528282, 4738235, 42321441, 378112132, 3379951089, 30211913537, 270034246073, 2413553512560, 21572510872955, 192816992434886, 1723410496604699, 15403947766639408, 137681484497162534
Offset: 1
Some solutions for n=5
..0..1..1..0. .1..0..1..0. .0..0..1..0. .0..1..0..1. .1..0..0..0
..1..0..1..0. .1..0..1..0. .0..0..1..0. .0..1..0..1. .1..0..0..0
..1..0..1..1. .1..0..0..0. .0..0..0..0. .1..0..0..0. .1..0..0..0
..0..0..0..1. .1..0..0..0. .0..0..0..1. .1..0..1..0. .1..0..0..0
..1..1..0..0. .0..1..1..1. .0..0..1..1. .1..1..1..0. .1..1..0..0
A295037
Number of nX5 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 2 1s.
Original entry on oeis.org
12, 280, 3853, 59126, 898493, 13706771, 209181266, 3184995895, 48548926944, 740019106008, 11277857830329, 171883749077632, 2619682437092951, 39926222792932513, 608509663116604097, 9274219880373144746
Offset: 1
Some solutions for n=4
..0..1..1..1..1. .0..0..1..1..0. .0..0..1..1..1. .0..0..1..1..0
..1..1..0..0..0. .1..1..0..1..0. .0..0..0..0..1. .0..0..0..0..1
..1..0..1..1..1. .0..1..0..0..0. .0..1..1..0..0. .0..1..0..0..1
..1..0..1..0..1. .0..1..1..0..0. .0..0..0..0..0. .0..1..0..0..0
A295038
Number of nX6 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 2 1s.
Original entry on oeis.org
21, 876, 19956, 528282, 13706771, 355281224, 9248214732, 240292442848, 6243986963713, 162252303626409, 4216381439247094, 109570922468132003, 2847344541437365138, 73992200911927723171, 1922796991924326509127
Offset: 1
Some solutions for n=3
..1..0..0..1..0..0. .1..1..0..1..1..1. .0..0..0..1..0..1. .0..0..0..0..0..1
..1..0..0..1..1..0. .1..0..1..0..0..1. .1..1..0..1..0..1. .0..1..0..1..0..1
..1..0..0..0..1..0. .0..0..1..0..0..0. .0..1..0..0..0..0. .1..1..0..1..0..0
A295039
Number of nX7 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 2 1s.
Original entry on oeis.org
37, 2735, 104096, 4738235, 209181266, 9248214732, 411280569141, 18227207589288, 807975522778623, 35828949243544333, 1588724655137268304, 70444327993290622210, 3123514826860958239480, 138498446900583005504125
Offset: 1
Some solutions for n=3
..0..0..0..1..1..1..0. .0..0..1..1..0..0..0. .1..1..0..0..0..0..0
..0..0..0..0..0..1..0. .1..0..0..0..0..1..1. .1..1..0..1..1..1..0
..1..1..0..0..0..1..0. .1..1..1..1..0..0..1. .0..0..0..0..0..1..1
A295034
Number of n X n 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 2 1's.
Original entry on oeis.org
1, 10, 140, 6686, 898493, 355281224, 411280569141, 1377458578461777, 13439667379225204666, 381706479329790703639253, 31542814403404743062254741113, 7585239934805237805543429969496485
Offset: 1
Some solutions for n=4:
..0..1..1..0. .1..1..1..1. .1..0..0..0. .0..0..0..1. .1..0..1..1
..0..0..1..1. .1..0..0..1. .1..0..0..0. .0..0..1..1. .1..0..1..0
..1..0..0..1. .0..0..0..0. .1..0..0..0. .1..0..1..0. .0..0..0..1
..1..1..0..1. .0..1..1..1. .0..0..0..0. .1..1..0..0. .0..1..1..1
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