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A071334 Number of polyiamonds with n cells without holes that do not tile the plane. 4
0, 0, 0, 0, 0, 0, 1, 0, 20, 103, 594, 1192, 6290, 18099, 54808, 159048, 502366, 1374593, 4076218, 11378831, 32674779, 93006494, 264720498, 748062099, 2134512296, 6071524897, 17289205132, 49268564671, 140605019208, 401392287316 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,9
COMMENTS
From Bernard Schott, Feb 21 2020: (Start)
There exist 112 polyiamonds without holes that have from 1 to 8 cells (A070765), but only one of these polyiamonds, corresponding to a(7)= 1 cannot tile the plane. This polyiamond is called V-shaped heptiamond (see proof in Martin Gardner's link in German).
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(End)
REFERENCES
M. Gardner, Tiling with Polyominoes, Polyiamonds and Polyhexes. Chap. 14 in Time Travel and Other Mathematical Bewilderments. New York: W. H. Freeman, pp. 175-187, 1988.
LINKS
Martin Gardner, V-heptiamond, Mathematisches Labyrinth: Neue Probleme für die Knobelgemeinde, p. 118, Google books.
Craig S. Kaplan, Heesch Numbers of Unmarked Polyforms, arXiv:2105.09438 [cs.CG], 2021. See Table 5 and Table 6.
Joseph Myers, Polyiamond tiling
MATHEMATICA
A[s_Integer] := With[{s6 = StringPadLeft[ToString[s], 6, "0"]}, Cases[ Import["https://oeis.org/A" <> s6 <> "/b" <> s6 <> ".txt", "Table"], {_, _}][[All, 2]]];
A000577 = A@000577;
A070764 = A@070764;
A071332 = A@071332;
a[n_] := A000577[[n]] - A070764[[n]] - A071332[[n]];
a /@ Range[30] (* Jean-François Alcover, Feb 21 2020 *)
CROSSREFS
Sequence in context: A113599 A077757 A126859 * A241355 A220207 A189950
KEYWORD
nonn,hard,more
AUTHOR
Joseph Myers, May 19 2002
EXTENSIONS
More terms from Joseph Myers, Nov 11 2003
a(29) and a(30) from Joseph Myers, Nov 21 2010
STATUS
approved

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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)