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 A007219 M5204 #60 Feb 16 2025 08:32:31
%S A007219 1,28,2108,227322,30276740,4541771016,739092675672,127674038970623,
%T A007219 23085759901610016,4327973308197103600,835531767841066680300,
%U A007219 165266721954751746697155,33364181616540879268092840
%N A007219 Number of golygons of order 8n (or serial isogons of order 8n).
%C A007219 A golygon of order N is a closed path along the streets of the Manhattan grid with successive edge lengths of 1,2,3,...,N (returning to the starting point after the edge of length N), and which makes a 90-degree turn (left or right) after each edge.
%C A007219 It is known that the order N must be a multiple of 8.
%D A007219 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A007219 I. Vardi, Computational Recreations in Mathematica. Addison-Wesley, Redwood City, CA, 1991, p. 92.
%H A007219 Vaclav Kotesovec, <a href="/A007219/b007219.txt">Table of n, a(n) for n = 1..100</a>
%H A007219 A. K. Dewdney, <a href="https://www.jstor.org/stable/24996874">An odd journey along even roads leads to home in Golygon City</a>, Mathematical Recreations Column, Scientific American, July 1990, pp. 118-121.
%H A007219 A. K. Dewdney, <a href="/A007219/a007219.png">Illustration of the unique golygon of order 8</a>, from the article "An odd journey along even roads leads to home in Golygon City", Mathematical Recreations Column, Scientific American, July 1990, pp. 118-121.
%H A007219 A. K. Dewdney, <a href="/A007219/a007219_1.png">Illustration of the 28 golygons of order 16</a>, from the article "An odd journey along even roads leads to home in Golygon City", Mathematical Recreations Column, Scientific American, July 1990, pp. 118-121.
%H A007219 Adam P. Goucher, <a href="http://cp4space.wordpress.com/2014/04/30/golygons-and-golyhedra/">Golygons and golyhedra</a>
%H A007219 L. Sallows, M. Gardner, R. K. Guy and D. E. Knuth, <a href="http://www.jstor.org/stable/2690648">Serial isogons of 90 degrees</a>, Math. Mag. 64 (1991), 315-324.
%H A007219 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Golygon.html">Golygon</a>
%F A007219 a(n) = A006718(n)/4. - _Charles R Greathouse IV_, Apr 29 2012
%F A007219 a(n) ~ 3*2^(8*n-6)/(Pi*n^2*(4*n+1)). - _Vaclav Kotesovec_, Dec 09 2013
%t A007219 p1[n_] := Product[x^k + 1, {k, 1, n - 1, 2}] // Expand; p2[n_] := Product[x^k + 1, {k, 1, n/2}] // Expand; c[n_] := Coefficient[p1[n], x, n^2/8] * Coefficient[p2[n], x, n (n/2 + 1)/8]; a[n_] := c[8*n]/4; Table[a[n], {n, 1, 13}] (* _Jean-François Alcover_, Jul 24 2013, after _Eric W. Weisstein_ *)
%Y A007219 Cf. A060005, A107350.
%Y A007219 See also A006718.
%K A007219 nonn,easy,nice
%O A007219 1,2
%A A007219 _Simon Plouffe_
%E A007219 Two more terms from _N. J. A. Sloane_ (from the reference), May 23 2005