A251376 Number of (n+1)X(3+1) 0..3 arrays with every 2X2 subblock summing to 5 6 or 7

9124, 385704, 17309672, 796635224, 37078015004, 1734708707700, 81356563852940, 3819965043029148, 179459290594576812, 8433120201697489676, 396339147306043331956, 18628300842155979771596, 875574504616798793124900

Offset

1,1

Comments

Column 3 of A251381

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

R. H. Hardin, Empirical recurrence of order 52

Robert Israel, Maple-assisted proof of empirical recurrence

Formula

Empirical recurrence of order 52 (see link above)

Empirical recurrence verified (see link). - Robert Israel, Aug 22 2019

Example

Some solutions for n=1
..2..2..0..1....1..1..1..3....2..2..2..0....3..1..3..0....1..2..1..1
..0..2..2..2....1..3..1..0....3..0..3..2....3..0..1..3....1..1..2..3

Maple

Rows:= [seq(seq(seq(seq([a, b, c, d], a=0..3), b=0..3), c=0..3), d=0..3)]:
f:= proc(i, j) local S, k;
  S:= [seq(Rows[i][k]+Rows[i][k+1]+Rows[j][k]+Rows[j][k+1], k=1..3)];
  if min(S)>=5 and max(S)<=7 then 1 else 0 fi
end proc:
T:= Matrix(256, 256, f):
U[0]:= Vector(256, 1):
for j from 1 to 40 do U[j]:= T . U[j-1] od:
seq(U[0]^%T . U[j], j=1..40); # Robert Israel, Aug 22 2019

Crossrefs

Sequence in context: A233713 A174983 A184381 * A253031 A093213 A205922

Adjacent sequences: A251373 A251374 A251375 * A251377 A251378 A251379

Keyword

nonn

Author

R. H. Hardin, Dec 01 2014

Status

approved