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A194772
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Number of lower triangles of an (n+2) X (n+2) 0..2 array with new values introduced in row major order 0..2 and no element unequal to more than one horizontal or vertical neighbor.
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1
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7, 17, 41, 95, 219, 493, 1101, 2427, 5311, 11529, 24881, 53399, 114083, 242725, 514581, 1087411, 2291335, 4815681, 10097401, 21126863, 44117867, 91963997, 191384541, 397682155, 825190479, 1710033273, 3539371201, 7317351687
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = 3*a(n-1) +a(n-2) -7*a(n-3) +4*a(n-5).
G.f.: x*(7 - 4*x - 17*x^2 + 4*x^3 + 12*x^4) / ((1 - x)*(1 + x)^2*(1 - 2*x)^2).
a(n) = (-3*n + 2^(n+3)*(3*n+8) + 17) / 27 for n even.
a(n) = (3*n + 2^(n+3)*(3*n+8) + 10) / 27 for n odd.
(End)
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EXAMPLE
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All solutions for 3 X 3 including a 2.
..0
..1.1
..1.1.2
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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