A275505 - OEIS

A275505

Number of 5 X n 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,0) or (-1,-1) and new values introduced in order 0..2.

12, 56, 232, 988, 4180, 17712, 75024, 317812, 1346268, 5702888, 24157816, 102334156, 433494436, 1836311904, 7778742048, 32951280100, 139583862444, 591286729880, 2504730781960, 10610209857724, 44945570212852

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OFFSET

1,1

LINKS

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

FORMULA

Empirical: a(n) = 3*a(n-1) + 5*a(n-2) + a(n-3).

Conjectures from Colin Barker, Feb 04 2019: (Start)

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

a(n) = (10*(-1)^n + (15-7*sqrt(5))*(2-sqrt(5))^n + (2+sqrt(5))^n*(15+7*sqrt(5))) / 10.

(End)

EXAMPLE

Some solutions for n=4:

..0..1..1..2. .0..1..2..0. .0..0..1..1. .0..1..1..2. .0..0..0..0

..0..1..2..0. .1..2..2..0. .0..1..2..2. .1..1..2..0. .1..1..1..1

..1..2..0..0. .1..2..0..1. .1..2..2..0. .2..2..0..0. .1..2..2..2

..1..2..0..1. .2..0..0..1. .2..2..0..1. .2..0..0..1. .2..2..0..0

..2..0..1..1. .0..0..1..2. .2..0..0..1. .1..1..1..2. .0..0..1..1

CROSSREFS

Row 5 of A275504.

Sequence in context: A009430 A348584 A035289 * A009827 A068418 A068414

Adjacent sequences: A275502 A275503 A275504 * A275506 A275507 A275508

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jul 30 2016

STATUS

approved