This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A056841 #65 Jul 02 2025 16:02:00 %S A056841 1,1,2,5,15,54,212,908,4011,18260,84320,394462,1860872,8843896, %T A056841 42275308,203113670,980101070,4747504560,23074132601 %N A056841 Number of diagonal polyominoes with n cells. %C A056841 Apparently the cells are circular blobs which must be connected diagonally and the polyominoes can be rotated by 90 degrees and turned over. %C A056841 Also the number of essentially different (i.e., not related by reflections, translations or rotations) diagrams consisting of n nodes in Z^2 and n-1 horizontal or vertical edges of length 1 between pairs of nodes such that the resulting graph is connected (hence a tree). - _Paul Boddington_, Jul 27 2004 %C A056841 They are thus equivalent to a subset of the polyedges, counted by A019988, i.e., those that are treelike. - _John Mason_, Aug 20 2021 %C A056841 The number of treelike polyedges with n edges is a(n+1). - _John Mason_, Feb 12 2023 %H A056841 R. J. Mathar, <a href="/A056841/a056841.gz">Table of all such polyominoes with n <= 10 cells</a> (gzipped) %H A056841 R. J. Mathar, <a href="/A056841/a056841.cpp.txt">C++ program</a> %H A056841 Douglas A. Torrance, <a href="https://arxiv.org/abs/1906.01541">Enumeration of planar Tangles</a>, arXiv:1906.01541 [math.CO], 2019-2020. See Table 4.1 (C). %H A056841 M. Vicher, <a href="http://www.vicher.cz/puzzle/polyforms.htm">Polyforms</a> %H A056841 M. Vicher, <a href="http://www.vicher.cz/puzzle/polyform/minio/images/d1.gif">The 15 5-celled diagonal polyominoes</a> %H A056841 M. Vicher, <a href="/A056841/a056841.gif">The 15 5-celled diagonal polyominoes</a> %F A056841 a(n+1) + A348095(n) = A019988(n). - _R. J. Mathar_, Sep 30 2021 %e A056841 The diagonal polyominoes with 1, 2, 3 and 4 cells are %e A056841 O O O O O %e A056841 \ \ \ / %e A056841 O O O %e A056841 \ %e A056841 O %e A056841 O O O O O O %e A056841 \ \ \ / \ / / %e A056841 O O O O O O O %e A056841 \ / \ \ / / %e A056841 O O O O O %e A056841 \ \ %e A056841 O O %Y A056841 See also A056840, A056787, A019988 (free polysticks), A348095 (with cycles). %K A056841 nonn,nice,more %O A056841 1,3 %A A056841 _James Sellers_, Aug 28 2000 %E A056841 Description revised by _N. J. A. Sloane_, Jun 21 2001 %E A056841 a(10) from _R. J. Mathar_, Apr 10 2006 %E A056841 a(11) from _Douglas A. Torrance_, Mar 06 2020 %E A056841 a(12)-a(14) from _John Mason_, Aug 14 2021 %E A056841 a(15)-a(19) from _John Mason_, Jun 01 2023