A197989 - OEIS

%I #21 Sep 12 2015 11:00:27

%S 1,4,45,886,24395,860336,36914493,1863645610,108131503623,

%T 7085585223652,517329551346608,41634263983867842,3661077644199252550,

%U 349191617521920855488,35902782820742394839453,3958207187579046500083794,465777357329812920074875295

%N Number of binary arrangements of total n 1's, without adjacent 1's on n X n array connected n-s

%H Vaclav Kotesovec, <a href="/A197989/b197989.txt">Table of n, a(n) for n = 1..108</a>

%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>, 6ed, p.373-381

%F Asymptotic (V. Kotesovec, Oct 15 2011): a(n) ~ n^(2n)/n!*exp(-3/2).

%t permopak[part_,k_]:=(hist=ConstantArray[0,k];

%t Do[hist[[part[[t]]]]++,{t,1,Length[part]}];

%t (Length[part])!/Product[(hist[[t]])!,{t,1,k}]);

%t waz1n[k_,n_]:=(If[n-k+1<k,0,Binomial[n-k+1,k]]);

%t semiwaz[k_,n_]:=(psum=0;

%t Do[p=IntegerPartitions[k,{size}];

%t psum=psum+Sum[permopak[p[[i]],k]*Binomial[n,Length[p[[i]]]]*Product[waz1n[p[[i,j]],n] ,{j,1,Length[p[[i]]]}], {i,1,Length[p]}],{size,1,n}];

%t psum);

%t Table[semiwaz[n,n],{n,1,25}]

%Y Cf. A067966, A197990.

%K nonn,nice,hard

%O 1,2

%A _Vaclav Kotesovec_, Oct 20 2011