

A007219


Number of serial isogons of order 8n (or Golygons).
(Formerly M5204)


4



1, 28, 2108, 227322, 30276740, 4541771016, 739092675672, 127674038970623, 23085759901610016, 4327973308197103600, 835531767841066680300, 165266721954751746697155, 33364181616540879268092840
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OFFSET

1,2


REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 1..100
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), 315324.


FORMULA

a(n) = A006718(n)/4.  Charles R Greathouse IV, Apr 29 2012
a(n) ~ 3*2^(8*n6)/(Pi*n^2*(4*n+1)).  Vaclav Kotesovec, Dec 09 2013


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}] (* JeanFrançois Alcover, Jul 24 2013, after Eric Weisstein *)


CROSSREFS

Cf. A107350, A060005.
Sequence in context: A182400 A197438 A202811 * A203751 A178187 A184134
Adjacent sequences: A007216 A007217 A007218 * A007220 A007221 A007222


KEYWORD

nonn,easy,nice


AUTHOR

Simon Plouffe


EXTENSIONS

Two more terms from N. J. A. Sloane (from the reference), May 23 2005


STATUS

approved



