A183401 Half the number of nX5 binary arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors

16, 18, 110, 1152, 8366, 72962, 592416, 4948658, 41522206, 347213952, 2919358170, 24526252242, 206222293760, 1734866624642, 14595269926750, 122816323809792, 1033547558771630, 8698080884070050, 73204345173096240, 616106711205094050

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: A278471 A223588 A358423 * A300142 A070574 A249612

Adjacent sequences: A183398 A183399 A183400 * A183402 A183403 A183404

Keyword

nonn

Author

R. H. Hardin, Jan 04 2011

Status

approved