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A277761 Number of n X 2 0..2 arrays with every element equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0) both plus 1 mod 3 and minus 1 mod 3, with new values introduced in order 0..2. 1
0, 1, 2, 14, 56, 284, 1304, 6248, 29408, 139472, 659360, 3121376, 14768000, 69887936, 330703232, 1564924544, 7405262336, 35042157824, 165821110784, 784674242048, 3713117739008, 17570663078912, 83145267845120, 393447636985856 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

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

FORMULA

Empirical: a(n) = 4*a(n-1) + 6*a(n-2) - 12*a(n-3).

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

G.f.: x^2*(1 - 2*x) / ((1 + 2*x)*(1 - 6*x + 6*x^2)).

a(n) = (3*(-1)^n*2^(2+n) - (-5+sqrt(3))*(3+sqrt(3))^n + (3-sqrt(3))^n*(5+sqrt(3))) / 132.

(End)

EXAMPLE

Some solutions for n=4:

..0..1. .0..1. .0..1. .0..1. .0..1. .0..1. .0..1. .0..1. .0..1. .0..1

..2..2. .2..2. .2..2. .2..2. .2..2. .2..2. .2..2. .2..2. .2..2. .2..2

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

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

CROSSREFS

Column 2 of A277767.

Sequence in context: A067056 A208428 A137482 * A203576 A178605 A212895

Adjacent sequences:  A277758 A277759 A277760 * A277762 A277763 A277764

KEYWORD

nonn

AUTHOR

R. H. Hardin, Oct 29 2016

STATUS

approved

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Last modified September 18 09:22 EDT 2020. Contains 337166 sequences. (Running on oeis4.)