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A183401 Half the number of nX5 binary arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors 1
16, 18, 110, 1152, 8366, 72962, 592416, 4948658, 41522206, 347213952, 2919358170, 24526252242, 206222293760, 1734866624642, 14595269926750, 122816323809792, 1033547558771630, 8698080884070050, 73204345173096240, 616106711205094050 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 5 of A183402

LINKS

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

Robert Israel, Linear recurrence of order 81 for n>=83

Robert Israel, Maple-assisted derivation of recurrence

FORMULA

Linear recurrence of order 81 for n >= 83 (see links). - Robert Israel, Oct 25 2019

EXAMPLE

Some solutions with a(1,1)=0 for 4X5

..0..0..1..1..1....0..1..0..0..1....0..0..0..0..0....0..1..0..0..0

..1..1..0..0..0....0..1..1..0..1....1..1..1..1..1....0..1..0..1..1

..0..0..0..1..1....0..1..0..0..1....1..0..0..1..1....1..1..0..1..0

..1..1..1..1..0....0..1..1..1..1....1..0..0..0..0....0..0..0..1..0

MAPLE

Configs:= [seq(convert(n, base, 2)[1..10], n=2^10..2^11-1)]:

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[6..10] <> Xj[1..5] then return 0 fi;

if Xi[6] = signum(Xi[2]+Xj[7]) then return 0 fi;

for k from 7 to 9 do if Xi[k] = signum(Xi[k-6]+Xi[k-4]+Xj[k-1]+Xj[k+1]) then return 0 fi od;

if Xi[10] = signum(Xi[4]+Xj[9]) then return 0 fi;

1

end proc:

T:= Matrix(1024, 1024, Compatible):

uok:= proc(i) local a, k;

   a:= map(t -> 2*t-1, Configs[i]);

   if a[1]=a[7] then return 0 fi;

   for k from 2 to 4 do if a[k] = signum(a[k+4]+a[k+6]) then return 0 fi od;

   if a[5]=a[9] then return 0 fi;

   1

end proc:

u:= Vector(1024, uok):

vok:= proc(i) local a, k;

   a:= map(t -> 2*t-1, Configs[i]);

   if a[6]=a[2] then return 0 fi;

   for k from 7 to 9 do if a[k] = signum(a[k-4]+a[k-6]) then return 0 fi od;

   if a[10]=a[4] then return 0 fi;

    1

end proc:

v:= Vector(1024, vok):

Tv[0]:= v:

for nn from 1 to 30 do Tv[nn]:= T . Tv[nn-1] od:

[32, seq(u^%T . Tv[n], n=0..30)]/2: # Robert Israel, Oct 25 2019

CROSSREFS

Cf. A183402.

Sequence in context: A308222 A278471 A223588 * A300142 A070574 A249612

Adjacent sequences:  A183398 A183399 A183400 * A183402 A183403 A183404

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jan 04 2011

STATUS

approved

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Last modified August 11 03:41 EDT 2022. Contains 356046 sequences. (Running on oeis4.)