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A183821 1/256 the number of (n+1) X 3 0..3 arrays with no 2 X 2 subblock being a reflection across the shared element pair of any horizontal or vertical neighbor. 1
15, 813, 43947, 2377341, 128578815, 6954559893, 376152548283, 20345104031589, 1100412240703119, 59518368554767389, 3219189893127084843, 174117402720326269485, 9417546276713264441151, 509369980225226329837125 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 2 of A183827.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..147

Robert Israel, Maple-assisted proof of formula

FORMULA

Empirical: a(n) = 43*a(n-1) + 645*a(n-2) - 2451*a(n-3).

Empirical g.f.: 3*x*(5 + 56*x - 229*x^2) / (1 - 43*x - 645*x^2 + 2451*x^3). - Colin Barker, Apr 05 2018

Empirical formulas verified (see link). - Robert Israel, Aug 10 2018

EXAMPLE

Some solutions with upper left block zero for 5 X 3:

   0 0 2   0 0 0   0 0 3   0 0 3   0 0 0   0 0 2   0 0 0

   0 0 0   0 0 1   0 0 3   0 0 2   0 0 1   0 0 1   0 0 2

   2 0 0   2 0 1   3 0 2   1 0 2   1 0 3   1 0 0   3 0 1

   2 2 1   3 2 3   1 3 1   1 3 1   0 3 3   2 1 2   0 3 3

   3 2 3   0 0 3   0 0 3   2 0 3   3 2 2   0 0 3   2 2 0

MAPLE

Configs:= remove(t -> [t[1], t[4]]=[t[3], t[6]], [seq(convert(4^6+i, base, 4)[1..6], i=0..4^6-1)]): nConfigs:= nops(Configs):

Compatible:= proc(i, j) local k;

if Configs[i][4..6] <> Configs[j][1..3] or Configs[i][1..2] =Configs[j][4..5] or Configs[i][2..3] = Configs[j][5..6] then 0 else 1 fi;

end proc:

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

u:= Vector(nConfigs, 1):

Tu[0]:= u:

for n from 1 to 30 do Tu[n]:= T . Tu[n-1] od:

seq(u^%T . Tu[n]/256, n=0..30); # Robert Israel, Aug 10 2018

CROSSREFS

Cf. A183827.

Sequence in context: A280310 A211104 A279493 * A301312 A230181 A187803

Adjacent sequences:  A183818 A183819 A183820 * A183822 A183823 A183824

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jan 07 2011

STATUS

approved

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Last modified July 17 08:42 EDT 2019. Contains 325098 sequences. (Running on oeis4.)