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 A005038 M2026 #47 Jan 26 2024 08:36:14
%S A005038 1,1,2,12,57,366,2340,16252,115940,854981,6444826,49554420,387203390,
%T A005038 3068067060,24604111560,199398960212,1631041938108,13451978877748,
%U A005038 111765327780200,934774244822704,7865200653146905
%N A005038 Number of nonequivalent dissections of a polygon into n pentagons by nonintersecting diagonals up to rotation.
%C A005038 Also, with a different offset, number of colored quivers in the 3-mutation class of a quiver of Dynkin type A_n. - _N. J. A. Sloane_, Jan 22 2013
%C A005038 Number of oriented polyominoes composed of n pentagonal cells of the hyperbolic regular tiling with Schläfli symbol {5,oo}. A stereographic projection of this tiling on the Poincaré disk can be obtained via the Christensson link. For oriented polyominoes, chiral pairs are counted as two. - _Robert A. Russell_, Jan 23 2024
%D A005038 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005038 G. C. Greubel, <a href="/A005038/b005038.txt">Table of n, a(n) for n = 1..1000</a>
%H A005038 Malin Christensson, <a href="http://malinc.se/m/ImageTiling.php">Make hyperbolic tilings of images</a>, web page, 2019.
%H A005038 F. Harary, E. M. Palmer, R. C. Read, <a href="/A000108/a000108_20.pdf">On the cell-growth problem for arbitrary polygons, computer printout, circa 1974</a>
%H A005038 F. Harary, E. M. Palmer and R. C. Read, <a href="https://doi.org/10.1016/0012-365X(75)90041-2">On the cell-growth problem for arbitrary polygons</a>, Discr. Math. 11 (1975), 371-389.
%H A005038 Hermund A. Torkildsen, <a href="https://arxiv.org/abs/1004.4512">Colored quivers of type A and the cell-growth problem</a>, arXiv:1004.4512 [math.RT], 2010.
%H A005038 Hermund A. Torkildsen, <a href="https://doi.org/10.1142/S0219498812501332">Colored quivers of type A and the cell-growth problem</a>, J. Algebra and Applications, 12 (2013), #1250133. - From _N. J. A. Sloane_, Jan 22 2013
%F A005038 a(n) ~ 2^(8*n + 1/2) / (sqrt(Pi) * n^(5/2) * 3^(3*n + 5/2)). - _Vaclav Kotesovec_, Mar 13 2016
%F A005038 a(n) = A005040(n) + A369471(n) = 2*A005040(n) - A369472(n) = 2*A369471(n) + A369472(n). - _Robert A. Russell_, Jan 23 2024
%t A005038 p=5; Table[Binomial[(p-1)n, n]/(((p-2)n+1)((p-2)n+2)) +If[OddQ[n], 0, Binomial[(p-1)n/2, n/2]/((p-2)n+2)]+Plus @@ Map[EulerPhi[ # ]Binomial[((p-1)n+1)/#, (n-1)/# ]/((p-1)n+1)&, Complement[Divisors[GCD[p, n-1]], {1}]], {n, 1, 20}] (* _Robert A. Russell_, Dec 11 2004 *)
%Y A005038 Column k=5 of A295224.
%Y A005038 Polyominoes: A005040 (unoriented), A369471 (chiral), A369472 (achiral), A001683(n+2) {3,oo}, A005034 {4,oo}, A221184{n-1} {6,oo}.
%K A005038 nonn,easy
%O A005038 1,3
%A A005038 _N. J. A. Sloane_
%E A005038 a(21) corrected by _Sean A. Irvine_, Mar 11 2016
%E A005038 Name edited by _Andrew Howroyd_, Nov 20 2017