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A196013
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Number of n X 4 0..4 arrays with each element equal to the number its horizontal and vertical neighbors within one of itself.
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1
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1, 1, 7, 25, 27, 91, 231, 455, 1135, 2693, 6041, 14257, 33349, 76941, 179553, 418345, 971503, 2261807, 5264419, 12243481, 28490729, 66295633, 154236017, 358872825, 835013523, 1942797397, 4520363539, 10517663443, 24471508585, 56938341019
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OFFSET
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1,3
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COMMENTS
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Column 4 of A196017.
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..200
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FORMULA
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Empirical: a(n) = a(n-1) +2*a(n-2) +4*a(n-3) -a(n-4) -4*a(n-5) -2*a(n-6) -3*a(n-7) -3*a(n-8) +a(n-10) for n>14.
Empirical g.f.: x*(1 + 4*x^2 + 12*x^3 - 15*x^4 - 9*x^5 - x^6 - 8*x^7 + x^8 - 3*x^9 + 2*x^10+ 6*x^11 + 2*x^12 - 2*x^13) / (1 - x - 2*x^2 - 4*x^3 + x^4 + 4*x^5 + 2*x^6 + 3*x^7 + 3*x^8 - x^10). - Colin Barker, May 08 2018
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EXAMPLE
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Some solutions for n=5:
..2..3..3..2....2..2..3..2....2..3..2..2....2..2..2..0....2..2..3..2
..3..4..4..3....2..0..3..3....2..3..0..2....2..0..3..2....2..0..3..3
..3..4..3..3....3..3..3..3....0..3..2..3....3..3..4..3....3..3..3..3
..3..3..0..2....2..3..0..2....2..3..0..2....3..4..4..3....3..3..0..2
..2..3..2..2....0..2..2..2....2..3..2..2....2..3..3..2....2..3..2..2
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CROSSREFS
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Cf. A196017.
Sequence in context: A246792 A178370 A034125 * A272366 A327107 A075926
Adjacent sequences: A196010 A196011 A196012 * A196014 A196015 A196016
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin, Sep 26 2011
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STATUS
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approved
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