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A234006
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Free polyominoes with 2n squares, having reflectional symmetry on axis that coincides with edges.
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5
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1, 2, 4, 11, 35, 114, 392, 1381, 4998, 18292, 67791, 253182, 952527, 3603389, 13699516, 52300071, 200406183, 770424072, 2970400815, 11482442855, 44491876993, 172766491178, 672186631950, 2619995178793, 10228902801505, 39996341268584, 156612023001490, 614044347934591
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OFFSET
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1,2
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COMMENTS
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The number of free polyominoes of size 2n that have reflectional symmetry on a horizontal or vertical axis that coincides with the edges of some of the squares. The sequence is defined for 2n rather than n as odd-sized polyominoes cannot have the required symmetry.
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LINKS
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Table of n, a(n) for n=1..28.
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FORMULA
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a(2*n+1) = A151525(2*n+1), a(2*n) = A151525(2*n) + A182645(n) - A001168(n). - Andrew Howroyd, Dec 05 2018
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MATHEMATICA
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A151525 = Cases[Import["https://oeis.org/A151525/b151525.txt", "Table"], {_, _}][[All, 2]];
A182645 = Cases[Import["https://oeis.org/A182645/b182645.txt", "Table"], {_, _}][[All, 2]];
A001168 = Cases[Import["https://oeis.org/A001168/b001168.txt", "Table"], {_, _}][[All, 2]];
a[n_] := If[OddQ[n], A151525[[n]], A151525[[n]] + A182645[[n/2]] - A001168[[n/2]]];
Array[a, 28] (* Jean-François Alcover, Sep 10 2019, after Andrew Howroyd *)
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CROSSREFS
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Cf. A000105, A001168, A001933, A151525, A182645, A234007, A234008, A234009, A234010.
Sequence in context: A076321 A000088 A071794 * A285002 A340338 A107378
Adjacent sequences: A234003 A234004 A234005 * A234007 A234008 A234009
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KEYWORD
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nonn
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AUTHOR
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John Mason, Dec 18 2013
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EXTENSIONS
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a(12)-a(28) from Andrew Howroyd, Dec 05 2018
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STATUS
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approved
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