A006718 Number of golygons of length 8n.

1, 4, 112, 8432, 909288, 121106960, 18167084064, 2956370702688, 510696155882492, 92343039606440064, 17311893232788414400, 3342127071364266721200, 661066887819006986788620, 133456726466163517072371360

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

A007219 is the main entry for golygons.

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

• Seiichi Manyama, Table of n, a(n) for n = 0..200
• Eric Weisstein's World of Mathematics, Golygon

Crossrefs

Cf. A060468, A063865, A292476.

See A007219 for much more information about golygons.

Programs

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]; Table[a[n], {n, 0, 11}] (* Jean-François Alcover, Jul 24 2013, after Eric W. Weisstein *)

Formula

a(n) = 4 * A007219(n) for n > 0. - Charles R Greathouse IV, Apr 29 2012

a(n) = A060468(n) * A292476(2*n) = A063865(4*n) * A292476(2*n). - Seiichi Manyama, Sep 18 2017

Extensions

a(0) = 1 prepended by Seiichi Manyama, Sep 18 2017