A184033 1/16 the number of (n+1) X 4 0..3 arrays with all 2 X 2 subblocks having the same four values.

49, 61, 82, 124, 202, 358, 658, 1258, 2434, 4786, 9442, 18754, 37282, 74338, 148258, 296098, 591394, 1181986, 2362402, 4723234, 9443362, 18883618, 37761058, 75515938, 151019554, 302026786, 604028962, 1208033314, 2416017442, 4831985698

Offset

1,1

Comments

Column 3 of A184039.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4).

Conjectures from Colin Barker, Apr 10 2018: (Start)

G.f.: x*(49 - 86*x - 101*x^2 + 172*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).

a(n) = 9*2^(n/2-1) + 9*2^(n-1) + 34 for n even.

a(n) = 9*2^(n-1) + 3*2^((n+1)/2) + 34 for n odd.

(End)

Example

Some solutions for 3 X 4:
..0..0..1..2....0..1..0..1....0..2..3..2....2..2..2..2....1..3..1..3
..1..2..0..0....3..2..3..2....3..0..0..0....0..0..0..0....3..2..3..2
..0..0..1..2....1..0..1..0....0..2..3..2....2..2..2..2....1..3..1..3

Crossrefs

Cf. A184039.

Sequence in context: A039472 A135145 A111327 * A178951 A202001 A038640

Adjacent sequences: A184030 A184031 A184032 * A184034 A184035 A184036

Keyword

nonn

Author

R. H. Hardin, Jan 08 2011

Status

approved