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A266076
Number of n X 3 integer arrays with each element equal to the number of horizontal and vertical neighbors differing from itself by exactly one.
1
2, 4, 4, 6, 5, 12, 10, 16, 21, 31, 42, 66, 89, 132, 191, 280, 407, 601, 873, 1281, 1875, 2748, 4024, 5902, 8642, 12667, 18562, 27204, 39866, 58431, 85627, 125494, 183918, 269545, 395034, 578955, 848492, 1243527, 1822475, 2670967, 3914489, 5736967
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = a(n-1) + a(n-3) + a(n-6) - a(n-7) - a(n-9).
Empirical g.f.: x*(2 + 2*x - 5*x^4 + 3*x^5 - 10*x^6 - x^7 - 7*x^8) / ((1 - x)*(1 + x)*(1 - x + x^2)*(1 + x + x^2)*(1 - x - x^3)). - Colin Barker, Jan 09 2019
EXAMPLE
All solutions for n=4:
..0..0..0....1..2..1....0..0..0....2..1..1....2..3..2....1..1..2
..2..3..2....1..2..1....0..0..0....1..1..2....3..4..3....2..1..1
..3..4..3....1..2..1....0..0..0....1..1..2....2..3..2....2..1..1
..2..3..2....1..2..1....0..0..0....2..1..1....0..0..0....1..1..2
CROSSREFS
Column 3 of A266081.
Sequence in context: A365264 A152782 A307119 * A074325 A058249 A340226
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 20 2015
STATUS
approved