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A230825
Number of n X 2 0..3 arrays x(i,j) with each element horizontally, vertically or antidiagonally next to at least one element with value (x(i,j)+1) mod 4 and at least one element with value (x(i,j)-1) mod 4, no adjacent elements equal, and upper left element zero.
1
0, 2, 2, 6, 16, 44, 124, 354, 1020, 2956, 8598, 25066, 73180, 213838, 625196, 1828502, 5348922, 15649258, 45788486, 133980160, 392046972, 1147212852, 3357028498, 9823567212, 28746526324, 84120672526, 246161907322, 720343138052
OFFSET
1,2
LINKS
FORMULA
Empirical: a(n) = 4*a(n-1) - 2*a(n-2) - 3*a(n-3) - a(n-4) for n>5.
Empirical g.f.: 2*x^2*(1 - x)*(1 - 2*x - x^2) / (1 - 4*x + 2*x^2 + 3*x^3 + x^4). - Colin Barker, Sep 22 2018
EXAMPLE
All solutions for n=4:
..0..3....0..1....0..1....0..3....0..1....0..3
..1..2....3..2....3..2....1..2....3..2....1..2
..0..1....0..3....1..0....0..3....0..1....3..0
..3..2....1..2....2..3....1..2....3..2....2..1
CROSSREFS
Column 2 of A230831.
Sequence in context: A067136 A180068 A034439 * A060165 A303150 A134295
KEYWORD
nonn
AUTHOR
R. H. Hardin, Oct 30 2013
STATUS
approved