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A071334 Number of polyiamonds with n cells without holes that do not tile the plane.

%I A071334 #25 Dec 04 2023 06:39:56
%S A071334 0,0,0,0,0,0,1,0,20,103,594,1192,6290,18099,54808,159048,502366,
%T A071334 1374593,4076218,11378831,32674779,93006494,264720498,748062099,
%U A071334 2134512296,6071524897,17289205132,49268564671,140605019208,401392287316
%N A071334 Number of polyiamonds with n cells without holes that do not tile the plane.
%C A071334 From _Bernard Schott_, Feb 21 2020: (Start)
%C A071334 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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%C A071334 (End)
%D A071334 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.
%H A071334 Martin Gardner, <a href="https://books.google.com/books?id=BeagBgAAQBAJ&amp;pg=PA239">V-heptiamond</a>, Mathematisches Labyrinth: Neue Probleme für die Knobelgemeinde, p. 118, Google books.
%H A071334 Craig S. Kaplan, <a href="https://isohedral.ca/heesch-numbers-of-unmarked-polyforms/">Heesch Numbers of Unmarked Polyforms</a>
%H A071334 Craig S. Kaplan, <a href="https://arxiv.org/abs/2105.09438">Heesch Numbers of Unmarked Polyforms</a>, arXiv:2105.09438 [cs.CG], 2021. See Table 5 and Table 6.
%H A071334 Joseph Myers, <a href="http://www.polyomino.org.uk/mathematics/polyform-tiling/">Polyiamond tiling</a>
%t A071334 A[s_Integer] := With[{s6 = StringPadLeft[ToString[s], 6, "0"]}, Cases[ Import["https://oeis.org/A" <> s6 <> "/b" <> s6 <> ".txt", "Table"], {_, _}][[All, 2]]];
%t A071334 A000577 = A@000577;
%t A071334 A070764 = A@070764;
%t A071334 A071332 = A@071332;
%t A071334 a[n_] := A000577[[n]] - A070764[[n]] - A071332[[n]];
%t A071334 a /@ Range[30] (* _Jean-François Alcover_, Feb 21 2020 *)
%Y A071334 Equals A070765-A071332 and A071333-A070764, cf. A054361, A070768.
%K A071334 nonn,hard,more
%O A071334 1,9
%A A071334 _Joseph Myers_, May 19 2002
%E A071334 More terms from _Joseph Myers_, Nov 11 2003
%E A071334 a(29) and a(30) from _Joseph Myers_, Nov 21 2010