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%I #11 Oct 01 2021 17:11:01
%S 3,5,9,17,37,81,197,477,1197,3077,7989,20649,53885,140601,366917,
%T 959685,2511477,6571681,17202449,45027677,117871345,308581637,
%U 807852685,2114904397,5536838045,14495554593,37949503089,99352690141,260108204933
%N Degree of denominator of GF for number of ways to place k nonattacking queens on an n X n 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, May 31 2010), for k>1 : d(k) = 2*k+1+Sum[Sum[2*j*EulerPhi[i],{i,Fibonacci[k-j]+1,Fibonacci[k-j+1]}],{j,1,k-1}].
%F Asymptotic formula: d(k) ~ 6/(5*Pi^2)*((1+Sqrt[5])/2)^(2*k+1) or d(k) ~ 3*(1+Sqrt[5])/Pi^2*Fibonacci[k]^2.
%t Table[2*k + 1 + Sum[Sum[2*j*EulerPhi[i], {i, Fibonacci[k - j] + 1, Fibonacci[k - j + 1]}], {j, 1, k - 1}], {k, 1, 20}]
%Y Cf. A036464, A047659, A061994, A108792, A176186, A000010, A000045.
%K nonn
%O 1,1
%A _Vaclav Kotesovec_, Jun 07 2010