A006718 Number of golygons of length 8n. (Formerly M3707)

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

Offset

0,2

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

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

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 *)

Crossrefs

Cf. A060468, A063865, A292476.

See A007219 for much more information about golygons.

Sequence in context: A361543 A221625 A013151 * A185320 A293158 A196458

Adjacent sequences: A006715 A006716 A006717 * A006719 A006720 A006721

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

Status

approved