cp's OEIS Frontend

A006534 Number of one-sided triangular polyominoes (n-iamonds) with n cells; turning over not allowed, holes are allowed.

%I A006534 M3287 #45 Feb 16 2025 08:32:30
%S A006534 1,1,1,4,6,19,43,120,307,866,2336,6588,18373,52119,147700,422016,
%T A006534 1207477,3471067,9999135,28893560,83665729,242826187,706074369,
%U A006534 2056870697,6001555275,17538335077,51323792789,150390053432,441210664337,1295886453860,3810208448847,11214076720061,33035788241735
%N A006534 Number of one-sided triangular polyominoes (n-iamonds) with n cells; turning over not allowed, holes are allowed.
%C A006534 The figures are formed by connecting n regular triangles by edges.
%C A006534 "Turning over not allowed" means that axial symmetric polyiamonds are counted separately, thus a(4) = 4 and a(5) = 6 while A000577(4) = 3 and A000577(5) = 4, cf. examples. - _M. F. Hasler_, Nov 12 2017
%D A006534 F. Harary, Graphical enumeration problems; in Graph Theory and Theoretical Physics, ed. F. Harary, Academic Press, London, 1967, pp. 1-41.
%D A006534 W. F. Lunnon, Counting hexagonal and triangular polyominoes, pp. 87-100 of R. C. Read, editor, Graph Theory and Computing. Academic Press, NY, 1972.
%D A006534 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A006534 P. J. Torbijn, Polyiamonds, J. Rec. Math. 2 (1969), 216-227.
%H A006534 John Mason, <a href="/A006534/b006534.txt">Table of n, a(n) for n = 1..52</a>
%H A006534 R. K. Guy, <a href="http://www.g4g4.com/contentsmmpp.html">O'Beirne's Hexiamond</a>, in The Mathemagician and the Pied Puzzler - A Collection in Tribute to Martin Gardner, Ed. E. R. Berlekamp and T. Rogers, A. K. Peters, 1999, 85-96.
%H A006534 J. Meeus & N. J. A. Sloane, <a href="/A006532/a006532_1.pdf">Correspondence, 1974-1975</a>
%H A006534 Ed Pegg, Jr., <a href="http://demonstrations.wolfram.com/PolyformExplorer/">Illustrations of polyforms</a>
%H A006534 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Polyiamond.html">Polyiamond.</a>
%e A006534 From _M. F. Hasler_, Nov 12 2017: (Start)
%e A006534 Putting dots for the approximate center of the regular triangles (alternatively flipped up and down for neighboring dots), we have:
%e A006534 a(4) = #{ .... , .:. , ..: , :.. } = 4, while ..: and :.. are considered equivalent and not counted twice in A000577(4) = 3.
%e A006534 a(5) = #{ ..... , ...: , :... , ..:. , .:.. , :.: } = 6, and again the 2nd & 3rd and 4th & 5th are considered equivalent and not counted twice in A000577(5) = 4. (End)
%Y A006534 Cf. A000577 (same with "turning over allowed"), A030223, A030224, A001420.
%K A006534 nonn,hard,nice
%O A006534 1,4
%A A006534 _N. J. A. Sloane_
%E A006534 Corrected and extended by _David W. Wilson_
%E A006534 a(19) from _Achim Flammenkamp_, Feb 15 1999
%E A006534 a(20) to a(28) from _Joseph Myers_, Sep 24 2002
%E A006534 Edited by _M. F. Hasler_, Nov 12 2017
%E A006534 More terms from _John Mason_, Oct 28 2023