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 A103469 #32 Sep 25 2022 10:36:46
%S A103469 1,2,2,3,2,3,3,4,4,5,4,5,5,6,6,7,6,7,7,8,8,9,8,9,9,10,10,11,10,11,11,
%T A103469 12,12,13,12,13,13,14,14,15,14,15,15,16,16,17,16,17,17,18,18,19,18,19,
%U A103469 19,20,20,21,20,21,21,22,22,23,22,23,23,24,24,25,24,25,25,26,26,27,26,27
%N A103469 Number of polyominoes consisting of 3 regular unit n-gons.
%C A103469 Conjecture: if n > 3, then a(n + 3) is the number of connected components of the subgraph that is vertex-induced on Collatz's graph by the vertex subset {1, ..., n} (see Problem 3.11 of my article, available from the links). - _Lorenzo Sauras Altuzarra_, Apr 07 2020 [Corrected by _Pontus von Brömssen_, Jan 22 2021]
%H A103469 Colin Barker, <a href="/A103469/b103469.txt">Table of n, a(n) for n = 3..1000</a>
%H A103469 M. Koch and S. Kurz, <a href="http://arXiv.org/abs/math.CO/0605144">Enumeration of generalized polyominoes</a>, arXiv:math/0605144 [math.CO], 2006.
%H A103469 S. Kurz, <a href="http://www.mathe2.uni-bayreuth.de/sascha/oeis/k-polyominoes.html">k-polyominoes</a>.
%H A103469 Lorenzo Sauras Altuzarra, <a href="https://arxiv.org/abs/2002.03075">Some arithmetical problems that are obtained by analyzing proofs and infinite graphs</a>, arXiv:2002.03075 [math.NT], 2020.
%H A103469 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,1,-1).
%F A103469 a(n) = floor((n-2)/2) - floor((n-1)/6) + 1.
%F A103469 G.f.: -x^3*(x^6-x^5+x^4-x^3-x-1) / ((x-1)^2*(x+1)*(x^2-x+1)*(x^2+x+1)). - _Colin Barker_, Jan 19 2015
%e A103469 a(3)=1 because there is only one polyiamond consisting of 3 triangles and a(4)=2 because there are 2 polyominoes consisting of 3 squares.
%t A103469 LinearRecurrence[{1,0,0,0,0,1,-1},{1,2,2,3,2,3,3},80] (* _Harvey P. Dale_, Sep 18 2016 *)
%o A103469 (PARI) Vec(-x^3*(x^6-x^5+x^4-x^3-x-1)/((x-1)^2*(x+1)*(x^2-x+1)*(x^2+x+1)) + O(x^100)) \\ _Colin Barker_, Jan 19 2015
%Y A103469 Cf. A103470, A103471, A103472, A103473.
%K A103469 nonn,easy
%O A103469 3,2
%A A103469 _Sascha Kurz_, Feb 07 2005