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A178720 Degree of denominator of GF for number of ways to place k nonattacking queens on an n X n toroidal board. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 3 07:15 EST 2022. Contains 358512 sequences. (Running on oeis4.)