A234133 Number of (n+1) X (1+1) 0..3 arrays with every 2 X 2 subblock having the sum of the absolute values of all six edge and diagonal differences equal to 9.

32, 80, 192, 512, 1280, 3584, 9216, 26624, 69632, 204800, 540672, 1605632, 4259840, 12713984, 33816576, 101187584, 269484032, 807403520, 2151677952, 6450839552, 17196646400, 51573161984, 137506062336, 412451078144, 1099780063232

Offset

1,1

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 8*a(n-2) - 16*a(n-3).

Conjectures from Colin Barker, Oct 13 2018: (Start)

G.f.: 16*x*(2 + x - 14*x^2) / ((1 - 2*x)*(1 - 8*x^2)).

a(n) = 2^(3+n) + 2^(-1/2+(3*n)/2)*(4-4*(-1)^n + 3*sqrt(2) + 3*(-1)^n*sqrt(2)).

(End)

Example

Some solutions for n=5:
  3 3   0 0   0 3   3 1   3 0   1 1   0 0   3 0   3 0   3 2
  0 3   0 3   3 3   0 1   3 3   0 3   3 0   3 3   0 0   0 2
  1 1   0 0   0 3   1 3   0 3   0 0   1 1   3 0   3 0   2 3
  0 3   0 3   0 0   0 1   3 3   3 0   0 3   0 0   0 0   0 2
  2 2   2 2   0 3   3 1   0 3   1 1   2 2   0 3   3 0   2 3
  0 3   0 3   0 0   0 1   3 3   3 0   0 3   2 2   1 1   2 0

Crossrefs

Column 1 of A234140.

Sequence in context: A086047 A209378 A182466 * A203447 A340701 A043410

Adjacent sequences: A234130 A234131 A234132 * A234134 A234135 A234136

Keyword

nonn

Author

R. H. Hardin, Dec 19 2013

Status

approved