A183625 Number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock summing to 4.

45, 87, 189, 447, 1125, 2967, 8109, 22767, 65205, 189447, 556029, 1643487, 4881285, 14545527, 43439949, 129926607, 388993365, 1165407207, 3493075869, 10472936127, 31406225445, 94193510487, 282530199789, 847489936047, 2542268481525

Offset

1,1

Comments

Column 2 of A183632.

Links

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

Formula

Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3).

Conjectures from Colin Barker, Mar 30 2018: (Start)

G.f.: 3*x*(15 - 61*x + 54*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)).

a(n) = 3*(4 + 2^(2+n) + 3^n).

(End)

Example

Some solutions for 5 X 3:
  1 2 1    0 2 0    0 2 0    1 1 0    0 2 0    0 2 0    0 2 0
  1 0 1    2 0 2    1 1 1    1 1 2    2 0 2    0 2 0    0 2 0
  2 1 2    2 0 2    0 2 0    2 0 1    2 0 2    2 0 2    1 1 1
  0 1 0    1 1 1    1 1 1    1 1 2    2 0 2    2 0 2    2 0 2
  1 2 1    0 2 0    1 1 1    1 1 0    2 0 2    0 2 0    1 1 1

Crossrefs

Cf. A183632.

Sequence in context: A039361 A043964 A140380 * A184548 A184540 A115827

Adjacent sequences: A183622 A183623 A183624 * A183626 A183627 A183628

Keyword

nonn

Author

R. H. Hardin, Jan 06 2011

Status

approved