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A218836
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Unmatched value maps: number of n X 2 binary arrays indicating the locations of corresponding elements not equal to any horizontal or antidiagonal neighbor in a random 0..1 n X 2 array.
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9
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1, 2, 7, 21, 65, 200, 616, 1897, 5842, 17991, 55405, 170625, 525456, 1618192, 4983377, 15346786, 47261895, 145547525, 448227521, 1380359512, 4250949112, 13091204281, 40315615410, 124155792775, 382349636061, 1177482265857, 3626169232672, 11167134898976
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OFFSET
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0,2
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 0..210
Index entries for linear recurrences with constant coefficients, signature (2,3,1).
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FORMULA
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a(n) = 2*a(n-1) +3*a(n-2) +a(n-3).
G.f.: Q(0)/2 , where Q(k) = 1 + 1/(1- x*(4*k+2 +3*x+x^2)/(x*(4*k+4 +3*x+x^2) + 1/Q(k+1))); (continued fraction). - Sergei N. Gladkovskii, Oct 04 2013
G.f.: 1/(1-2*x-3*x^2-x^3). - Alois P. Heinz, Apr 21 2020
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EXAMPLE
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Some solutions for n=3
..1..1....1..1....0..0....1..0....0..0....1..0....0..0....1..1....0..0....1..0
..1..1....1..1....0..1....0..1....0..0....0..0....0..0....0..0....0..1....0..0
..1..1....0..0....0..0....1..1....0..1....1..1....1..1....1..1....1..1....0..1
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MAPLE
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a:= n-> (<<0|1|0>, <0|0|1>, <1|3|2>>^n. <<1, 2, 7>>)[1$2]:
seq(a(n), n=0..30); # Alois P. Heinz, Apr 21 2020
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CROSSREFS
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Column 2 of A218842.
Sequence in context: A106271 A027990 A037520 * A331722 A052911 A126133
Adjacent sequences: A218833 A218834 A218835 * A218837 A218838 A218839
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KEYWORD
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nonn,easy
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AUTHOR
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R. H. Hardin, Nov 07 2012
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EXTENSIONS
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a(0)=1 prepended and first g.f. adapted by Alois P. Heinz, Apr 21 2020
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STATUS
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approved
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