A276300 Number of 3 X n 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,1) or (0,-1) and new values introduced in order 0..2.

5, 11, 45, 173, 693, 2765, 11061, 44237, 176949, 707789, 2831157, 11324621, 45298485, 181193933, 724775733, 2899102925, 11596411701, 46385646797, 185542587189, 742170348749, 2968681394997, 11874725579981, 47498902319925

Offset

1,1

Links

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

Formula

Empirical: a(n) = 4*a(n-1) + a(n-2) - 4*a(n-3) for n>4.

Conjectures from Colin Barker, Feb 05 2019: (Start)

G.f.: x*(5 - 9*x - 4*x^2 + 2*x^3) / ((1 - x)*(1 + x)*(1 - 4*x)).

a(n) = (8 + 27*4^n) / 40 for n>1 and even.

a(n) = (72 + 27*4^n) / 40 for n>1 and odd.

(End)

Example

Some solutions for n=4:
..0..1..2..1. .0..1..0..1. .0..1..0..1. .0..1..0..2. .0..1..2..1
..0..1..2..0. .0..2..0..1. .2..1..2..1. .0..2..1..2. .0..1..2..0
..2..1..2..0. .0..2..0..2. .2..1..0..2. .1..2..0..2. .0..1..2..1

Crossrefs

Row 3 of A276299.

Sequence in context: A262020 A222368 A333114 * A222476 A097056 A092358

Adjacent sequences: A276297 A276298 A276299 * A276301 A276302 A276303

Keyword

nonn

Author

R. H. Hardin, Aug 28 2016

Status

approved