A184031 1/16 the number of (n+1) X 2 0..3 arrays with all 2 X 2 subblocks having the same four values.

16, 28, 49, 91, 169, 325, 625, 1225, 2401, 4753, 9409, 18721, 37249, 74305, 148225, 296065, 591361, 1181953, 2362369, 4723201, 9443329, 18883585, 37761025, 75515905, 151019521, 302026753, 604028929, 1208033281, 2416017409, 4831985665

Offset

1,1

Comments

Column 1 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*(16 - 20*x - 35*x^2 + 40*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).

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

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

(End)

Example

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

Crossrefs

Cf. A184039.

Sequence in context: A211570 A357264 A349418 * A206259 A064803 A220762

Adjacent sequences: A184028 A184029 A184030 * A184032 A184033 A184034

Keyword

nonn

Author

R. H. Hardin, Jan 08 2011

Status

approved