A184037 1/16 the number of (n+1) X 8 0..3 arrays with all 2 X 2 subblocks having the same four values.

625, 637, 658, 700, 778, 934, 1234, 1834, 3010, 5362, 10018, 19330, 37858, 74914, 148834, 296674, 591970, 1182562, 2362978, 4723810, 9443938, 18884194, 37761634, 75516514, 151020130, 302027362, 604029538, 1208033890, 2416018018, 4831986274

Offset

1,1

Comments

Column 7 of A184039.

Links

R. H. Hardin, Table of n, a(n) for n = 1..118

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*(625 - 1238*x - 1253*x^2 + 2476*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).

a(n) = 9*2^(n/2-1) + 9*2^(n-1) + 610 for n even.

a(n) = 9*2^(n-1) + 3*2^((n+1)/2) + 610 for n odd.

(End)

Example

Some solutions for 3 X 8:
..2..2..2..2..2..2..2..1....0..0..3..2..0..2..0..2....2..3..2..3..1..3..2..3
..3..1..3..1..3..1..3..2....3..2..0..0..3..0..3..0....1..2..1..2..2..2..1..2
..2..2..2..2..2..2..2..1....0..0..3..2..0..2..0..2....2..3..2..3..1..3..2..3

Crossrefs

Cf. A184039.

Sequence in context: A005081 A210115 A186484 * A186483 A043352 A223183

Adjacent sequences: A184034 A184035 A184036 * A184038 A184039 A184040

Keyword

nonn

Author

R. H. Hardin, Jan 08 2011

Status

approved