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A197237
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Number of n X 3 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 4,3,2,1,2 for x=0,1,2,3,4.
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1
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1, 5, 15, 46, 156, 507, 1637, 5338, 17401, 56648, 184384, 600287, 1954546, 6363740, 20718710, 67455328, 219621081, 715042212, 2328028685, 7579574414, 24677521267, 80344901649, 261586345777, 851670870944, 2772863697333, 9027869180467
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OFFSET
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1,2
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COMMENTS
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Every 0 is next to 0 4's, every 1 is next to 1 3's, every 2 is next to 2 2's, every 3 is next to 3 1's, every 4 is next to 4 2's.
Column 3 of A197242.
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..200
Robert Israel, Maple-assisted proof of empirical formula
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FORMULA
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Empirical: a(n) = 2*a(n-1) + 8*a(n-3) + 11*a(n-4) + 17*a(n-5) + 11*a(n-6) + 5*a(n-7) - 6*a(n-8) - 16*a(n-9) - 15*a(n-10) - 3*a(n-11) + a(n-13).
Empirical formula verified (see link). - Robert Israel, Sep 26 2018
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EXAMPLE
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Some solutions for n=4:
1 3 1 0 0 0 2 2 2 0 0 1 0 0 0 0 0 0 1 3 1
0 1 0 0 1 0 2 0 2 1 1 3 1 3 1 0 1 0 0 1 0
0 1 0 1 3 1 2 0 2 3 1 1 0 1 0 0 3 1 0 2 2
1 3 1 0 0 0 2 2 2 1 0 0 0 0 0 0 1 0 0 2 2
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MAPLE
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f:= gfun:-rectoproc({a(n) = 2*a(n-1) +8*a(n-3) +11*a(n-4) +17*a(n-5) +11*a(n-6) +5*a(n-7) -6*a(n-8) -16*a(n-9) -15*a(n-10) -3*a(n-11) +a(n-13), seq(a(i)=[1, 5, 15, 46, 156, 507, 1637, 5338, 17401, 56648, 184384, 600287, 1954546][i], i=1..13)}, a(n), remember):
map(f, [$1..30]); # Robert Israel, Sep 26 2018
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CROSSREFS
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Sequence in context: A058425 A079798 A037504 * A307242 A296545 A089040
Adjacent sequences: A197234 A197235 A197236 * A197238 A197239 A197240
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin, Oct 12 2011
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STATUS
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approved
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