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A265987 Number of n X 3 integer arrays with each element equal to the number of horizontal and antidiagonal neighbors not equal to itself. 1
2, 2, 6, 10, 30, 66, 182, 442, 1166, 2930, 7590, 19306, 49662, 126882, 325526, 833050, 2135150, 5467346, 14007942, 35877322, 91909086, 235418370, 603054710, 1544728186, 3956947022, 10135859762, 25963647846, 66507086890, 170361678270 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

FORMULA

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

Conjectures from Colin Barker, Jan 09 2019: (Start)

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

a(n) = 1 + (-((1-sqrt(17))/2)^n + ((1+sqrt(17))/2)^n) / sqrt(17).

(End)

EXAMPLE

Some solutions for n=4:

..1..3..2....1..3..1....0..0..0....1..3..2....1..3..2....1..3..1....1..3..2

..2..4..2....1..1..1....0..0..0....2..4..2....2..4..1....2..1..1....2..4..1

..2..4..2....2..4..2....0..0..0....1..1..1....2..1..1....1..4..2....1..1..1

..2..3..1....2..3..1....0..0..0....1..3..1....1..3..1....2..3..1....2..3..1

CROSSREFS

Column 3 of A265991.

Sequence in context: A265639 A208900 A229733 * A076907 A260785 A153897

Adjacent sequences:  A265984 A265985 A265986 * A265988 A265989 A265990

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 19 2015

STATUS

approved

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Last modified September 21 20:10 EDT 2021. Contains 347598 sequences. (Running on oeis4.)