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A330269
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The number of semi-meanders with n top arches and concentric arches within the starting arch or a starting arch with length one.
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1
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1, 1, 2, 4, 8, 18, 42, 108, 282, 786, 2192, 6402, 18600, 55978, 167256, 514102, 1567976, 4896164, 15170630, 47957260, 150468678, 480371736, 1522649458, 4900568718, 15665593150, 50761432998, 163431901126, 532624603680, 1725349278270, 5650796083020, 18401781369182
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OFFSET
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1,3
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LINKS
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FORMULA
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a(1) = 1, for n >= 2, a(n) = Sum_{k=1..n-1} A000682(k).
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EXAMPLE
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For n = 5, a(5) = 8:
/\ /\
//\\ /\ / \ /\
///\\\ /\ /\ / \ / /\\ /\ //\\
/\////\\\\, /\//\\//\\, /\/\//\/\\, /\//\//\\\, //\\///\\\,
/\
/\ //\\ starting arch
/\ /\ //\\ /\ ///\\\ (1) (2) (3) (4)
//\\//\\/\, ///\\\//\\, ////\\\\/\, 4 + 2 + 1 + 1 = 8.
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MATHEMATICA
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A000136 = Import["https://oeis.org/A000136/b000136.txt", "Table"][[All, 2]];
a[n_] := If[n == 1, 1, Sum[A000136[[k]]/k, {k, 1, n - 1}]];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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