A007219 Number of golygons of order 8n (or serial isogons of order 8n).
1, 28, 2108, 227322, 30276740, 4541771016, 739092675672, 127674038970623, 23085759901610016, 4327973308197103600, 835531767841066680300, 165266721954751746697155, 33364181616540879268092840
Offset: 1
References
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
- I. Vardi, Computational Recreations in Mathematica. Addison-Wesley, Redwood City, CA, 1991, p. 92.
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 1..100
- A. K. Dewdney, An odd journey along even roads leads to home in Golygon City, Mathematical Recreations Column, Scientific American, July 1990, pp. 118-121.
- A. K. Dewdney, Illustration of the unique golygon of order 8, 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.
- A. K. Dewdney, Illustration of the 28 golygons of order 16, 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.
- Adam P. Goucher, Golygons and golyhedra
- L. Sallows, M. Gardner, R. K. Guy and D. E. Knuth, Serial isogons of 90 degrees, Math. Mag. 64 (1991), 315-324.
- Eric Weisstein's World of Mathematics, Golygon
Programs
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Mathematica
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 *)
Formula
a(n) = A006718(n)/4. - Charles R Greathouse IV, Apr 29 2012
a(n) ~ 3*2^(8*n-6)/(Pi*n^2*(4*n+1)). - Vaclav Kotesovec, Dec 09 2013
Extensions
Two more terms from N. J. A. Sloane (from the reference), May 23 2005
Comments