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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 1
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

R. H. Hardin, Table of n, a(n) for n = 1..200

Robert Israel, Linear recurrence of order 93

Robert Israel, Maple-assisted derivation of recurrence

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

Adjacent sequences:  A183304 A183305 A183306 * A183308 A183309 A183310

KEYWORD

nonn

AUTHOR

R. H. Hardin Jan 03 2011

STATUS

approved

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Last modified January 20 10:55 EST 2022. Contains 350472 sequences. (Running on oeis4.)