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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

%I #7 Sep 12 2015 11:00:23

%S 3,8,12,28,58,142,350,906,2320,6056,15778,41024,107132,280184,732998,

%T 1918354,5019810,13141378,34398686,90045424,235729374,617126438,

%U 1615633560,4229774958,11073514332,28990794770,75898640094,198704554772

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

%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>, 6ed, 2013

%F 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

%t 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}]

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

%K nonn

%O 1,1

%A _Vaclav Kotesovec_, Jun 07 2010

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Last modified March 29 10:59 EDT 2024. Contains 371277 sequences. (Running on oeis4.)