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A183307 Half the number of nX6 binary arrays with no element equal to a strict majority of its horizontal and vertical neighbors 2
5, 14, 93, 572, 4212, 29400, 206755, 1447110, 10149621, 71244598, 500184679, 3512112015, 24658885220, 173129289198, 1215525172167, 8534122345666, 59917715208287, 420680331462689, 2953583636803146, 20737016295243029 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 6 of A183312
LINKS
FORMULA
Linear recurrence of order 93 for n >= 95: see links. - Robert Israel, Oct 23 2019
EXAMPLE
Some solutions with a(1,1)=0 for 6X4
..0..0..1..0....0..1..0..1....0..1..0..1....0..1..0..0....0..1..0..1
..1..1..0..1....1..0..1..0....0..1..0..0....1..0..1..1....1..1..0..1
..0..1..0..0....1..0..0..1....1..0..1..1....0..0..1..0....0..0..1..0
..1..0..1..1....0..1..1..0....0..1..1..0....1..1..0..1....1..1..0..1
..0..1..0..0....1..0..0..1....1..0..0..1....0..1..0..0....0..0..1..0
..1..0..1..1....1..0..1..0....0..1..1..0....1..0..1..1....1..0..1..0
MAPLE
Allowed:= proc(a)
if nops({a[1], a[2], a[7]})=1 or nops({a[1], a[2], a[3], a[8]})=1
or nops({a[2], a[3], a[4], a[9]})=1 or nops({a[3], a[4], a[5], a[10]})=1
or nops({a[4], a[5], a[6], a[11]})=1 or nops({a[5], a[6], a[12]})=1
or nops({a[1], a[7], a[8]})=1 or nops({a[2], a[7], a[8], a[9]})=1
or nops({a[3], a[8], a[9], a[10]})=1 or nops({a[4], a[9], a[10], a[11]})=1
or nops({a[5], a[10], a[11], a[12]})=1 or nops({a[6], a[11], a[12]})=1
then false else true fi
end proc:
Configs:= select(Allowed, [seq(convert(n, base, 2)[1..12], n=2^12..2^13-1)]):
Compatible:= proc(i, j) local Xi, Xj, k;
Xi:= map(t -> 2*t-1, Configs[i]); Xj:= map(t -> 2*t-1, Configs[j]);
if Xi[7..12] <> Xj[1..6] then return 0 fi;
if Xi[7] = signum(Xi[1]+Xi[8]+Xj[7]) then return 0 fi;
for k from 8 to 11 do if Xi[k] = signum(Xi[k-6]+Xi[k-1]+Xi[k+1]+Xj[k]) then return 0 fi od;
if Xi[12] = signum(Xi[6]+Xi[11]+Xj[12]) then return 0 fi;
1
end proc:
T:= Matrix(722, 722, Compatible):
uok:= proc(i) local a, k;
a:= map(t -> 2*t-1, Configs[i]);
for k from 2 to 5 do if a[k] = signum(a[k-1]+a[k+1]+a[k+6]) then return 0 fi od;
1
end proc:
u:= Vector(722, uok):
vok:= proc(i) local a, k;
a:= map(t -> 2*t-1, Configs[i]);
for k from 8 to 11 do if a[k] = signum(a[k-1]+a[k+1]+a[k-6]) then return 0 fi od;
1
end proc:
v:= Vector(722, vok):
Tv[0]:= v:
for nn from 1 to 50 do Tv[nn]:= T . Tv[nn-1] od:
A:= [10, seq(u^%T . Tv[n], n=0..50)]/2:
A[1..50]; # Robert Israel, Oct 23 2019
CROSSREFS
Sequence in context: A197797 A224245 A238380 * A334547 A348777 A024167
KEYWORD
nonn
AUTHOR
R. H. Hardin Jan 03 2011
STATUS
approved

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Last modified February 22 08:18 EST 2024. Contains 370240 sequences. (Running on oeis4.)