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A152113
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A001333 with terms repeated.
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4
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1, 1, 3, 3, 7, 7, 17, 17, 41, 41, 99, 99, 239, 239, 577, 577, 1393, 1393, 3363, 3363, 8119, 8119, 19601, 19601, 47321, 47321, 114243, 114243, 275807, 275807, 665857, 665857, 1607521, 1607521, 3880899, 3880899, 9369319, 9369319, 22619537, 22619537, 54608393
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OFFSET
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1,3
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COMMENTS
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Suggested by an email message from Hugo van der Sanden, Mar 23 2009, who says: Consider the partitions of a 2 x n rectangle into connected pieces consisting of unit squares cut along lattice lines. Then a(n) is the number of distinct pieces with rotational symmetry that extend to opposite corners.
a(n+2) is the number of palindromic words of length n on a 3-letter alphabet {a,b,c} which do not contain the "ab" subword. See A001906 for the words of length n on a 3-letter alphabet without "ab" subword but not necessarily palindromic. Example length 1: "a" or "b" or "c". Example length 2: "aa", "bb", "cc". Example length 3: There are 9 palindromic words but "aba" and "bab" are not admitted and only 7 remain. - R. J. Mathar, Jul 10 2019
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LINKS
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FORMULA
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a(n) = 2*a(n-2)+a(n-4). G.f.: -x*(x+1)*(x^2+1) / (x^4+2*x^2-1). - Colin Barker, Jul 14 2013
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EXAMPLE
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Example: the pieces illustrating a(3) = 3 are:
AAA BB. .CC
AAA .BB CC.
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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