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A151522
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Number of 1-sided polyrhombs with n cells.
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5
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1, 2, 4, 13, 35, 120, 392, 1405, 4998, 18378, 67792, 253509, 952534, 3604624, 13699554, 52304807, 200406370, 770442286, 2970401696, 11482513428, 44491881033, 172766765654, 672186650116, 2619996250930, 10228902882021, 39996345469572, 156612023354364, 614044364443761
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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Also counts 1-sided polyrects.
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LINKS
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John Mason, Table of n, a(n) for n = 1..48
Ed Pegg, Jr., Illustrations of polyforms
Eric Weisstein's World of Mathematics, Polyrhomb
Eric Weisstein's World of Mathematics, Polyrect
Wikipedia, Polyomino
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FORMULA
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a(n) = 4*A006749(n) + 2*A006746(n) + 2*A006748(n) + 4*A006747(n) + 2*A056877(n) + 2*A056878(n) + 2*A144553(n) + A142886(n). - Andrew Howroyd, Dec 04 2018
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MATHEMATICA
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A[n_] := With[{n6 = StringPadLeft[ToString[n], 6, "0"]}, Cases[ Import[ "https://oeis.org/A" <> n6 <> "/b" <> n6 <> ".txt", "Table"], {_, _}][[All, 2]]];
A006749 = A@6749; A006746 = A@6746; A006748 = A@6748; A006747 = A@6747; A056877 = A@56877; A056878 = A@56878; A144553 = A@144553; A142886 = A@142886;
a[n_] := 4*A006749[[n]] + 2*A006746[[n]] + 2*A006748[[n]] + 4*A006747[[n]] + 2*A056877[[n]] + 2*A056878[[n]] + 2*A144553[[n]] + A142886[[n + 1]];
a /@ Range[28] (* Jean-François Alcover, Jan 03 2020 *)
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CROSSREFS
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Polyominoes by group of symmetries relating shapes considered the same: A000105 (all symmetries), A001168 (translations only), A000988 (rotations and translations), A056780 (horizontal and vertical reflections, rotations of order 2 and translations), A056783 (reflections in either diagonal, rotations of order 2 and translations), A151522 (rotations of order 2 and translations), A151525 (reflections in a horizontal line and translations), A182645 (reflections in a NE-SW diagonal line and translations)
Sequence in context: A189590 A189597 A148235 * A148236 A148237 A148238
Adjacent sequences: A151519 A151520 A151521 * A151523 A151524 A151525
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KEYWORD
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nonn,hard
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AUTHOR
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Ed Pegg Jr, May 13 2009
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EXTENSIONS
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Edited and a(13)-a(18) by Joseph Myers, Nov 24 2010
a(19)-a(28) from Andrew Howroyd, Dec 04 2018
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STATUS
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approved
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