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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 (list; graph; refs; listen; history; text; internal format)
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), 315-324.

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

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-Fran├žois 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

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Last modified November 24 12:07 EST 2014. Contains 249898 sequences.