A197989 Number of binary arrangements of total n 1's, without adjacent 1's on n X n array connected n-s

1, 4, 45, 886, 24395, 860336, 36914493, 1863645610, 108131503623, 7085585223652, 517329551346608, 41634263983867842, 3661077644199252550, 349191617521920855488, 35902782820742394839453, 3958207187579046500083794, 465777357329812920074875295

Offset

1,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..108

V. Kotesovec, Non-attacking chess pieces, 6ed, p.373-381

Formula

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

Mathematica

permopak[part_, k_]:=(hist=ConstantArray[0, k];
Do[hist[[part[[t]]]]++, {t, 1, Length[part]}];
(Length[part])!/Product[(hist[[t]])!, {t, 1, k}]);
waz1n[k_, n_]:=(If[n-k+1<k, 0, Binomial[n-k+1, k]]);
semiwaz[k_, n_]:=(psum=0;
Do[p=IntegerPartitions[k, {size}];
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}];
psum);
Table[semiwaz[n, n], {n, 1, 25}]

Crossrefs

Cf. A067966, A197990.

Sequence in context: A107668 A214400 A360344 * A377830 A379700 A338456

Adjacent sequences: A197986 A197987 A197988 * A197990 A197991 A197992

Keyword

nonn,nice,hard

Author

Vaclav Kotesovec, Oct 20 2011

Status

approved