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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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
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 /@ Range[30] (* Jean-François Alcover, Feb 21 2020 *)
CROSSREFS
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