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 A071334 Number of polyiamonds with n cells without holes that do not tile the plane. 2
 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).   ____    ____   \  /\  /\  /    \/__\/__\/     \  /\  /      \/__\/ (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. 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 Equals A070765-A071332 and A071333-A070764, cf. A054361, A070768. Sequence in context: A113599 A077757 A126859 * A241355 A220207 A189950 Adjacent sequences:  A071331 A071332 A071333 * A071335 A071336 A071337 KEYWORD hard,nonn 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 August 12 17:17 EDT 2020. Contains 336439 sequences. (Running on oeis4.)