A178720 Degree of denominator of GF for number of ways to place k nonattacking queens on an n X n toroidal board.

3, 8, 12, 28, 58, 142, 350, 906, 2320, 6056, 15778, 41024, 107132, 280184, 732998, 1918354, 5019810, 13141378, 34398686, 90045424, 235729374, 617126438, 1615633560, 4229774958, 11073514332, 28990794770, 75898640094, 198704554772

Offset

1,1

Links

Table of n, a(n) for n=1..28.

V. Kotesovec, Non-attacking chess pieces, 6ed, 2013

Formula

Explicit formula (Vaclav Kotesovec, Jun 05 2010), for k>2 : t(k) = 4*k+Sum[Sum[(2*j+1)*EulerPhi[i],{i,2*Fibonacci[k-j-1]+1,2*Fibonacci[k-j]}],{j,1,k-2}], Asymptotic formula: t(k) ~ 12/(5*Pi^2)*((1+Sqrt[5])/2)^(2*k+1) or t(k) ~ 6*(1+Sqrt[5])/Pi^2*Fibonacci[k]^2

Mathematica

Table[If[k > 1, 4*k + Sum[ Sum[(2*j + 1)*EulerPhi[i], {i, 2*Fibonacci[k - j - 1] + 1, 2*Fibonacci[k - j]}], {j, 1, k - 2}], 3], {k, 1, 20}]

Crossrefs

A172517, A172518, A172519, A173775, A000010, A000045, A178717.

Sequence in context: A114803 A083171 A058582 * A027292 A032304 A032217

Adjacent sequences: A178717 A178718 A178719 * A178721 A178722 A178723

Keyword

nonn

Author

Vaclav Kotesovec, Jun 07 2010

Status

approved