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A290052 Number of X-rays of n X n binary matrices with exactly n ones.

%I A290052 #23 Nov 06 2017 09:07:00
%S A290052 1,1,4,23,139,860,5393,34142,217717,1396346,8997695,58205686,
%T A290052 377775385,2458841504,16043226825,104901986083,687221188145,
%U A290052 4509605878736,29636894936761,195035340954186,1285062484293880,8476508261617168,55969236979211755,369900194873712830
%N A290052 Number of X-rays of n X n binary matrices with exactly n ones.
%C A290052 The X-ray of a matrix is defined as the sequence of antidiagonal sums.
%H A290052 Alois P. Heinz, <a href="/A290052/b290052.txt">Table of n, a(n) for n = 0..1000</a>
%H A290052 C. Bebeacua, T. Mansour, A. Postnikov and S. Severini, <a href="https://arxiv.org/abs/math/0506334">On the X-rays of permutations</a>, arXiv:math/0506334 [math.CO], 2005.
%H A290052 <a href="/index/Mat#binmat">Index entries for sequences related to binary matrices</a>
%F A290052 A019589(n) <= a(n) <= A014062(n).
%F A290052 a(n) ~ c * 3^(3*n) / (2^(2*n) * sqrt(n)), where c = 0.153294749730773567280925277269616968259180871352428154276351832424636097919... - _Vaclav Kotesovec_, Jul 22 2017
%e A290052 a(0) = 1: [].
%e A290052 a(1) = 1: 1.
%e A290052 a(2) = 4: 011, 020, 101, 110.
%e A290052 a(3) = 23: 00021, 00111, 00120, 00201, 00210, 00300, 01011, 01020, 01101, 01110, 01200, 02001, 02010, 02100, 10011, 10020, 10101, 10110, 10200, 11001, 11010, 11100, 12000.
%p A290052 b:= proc(n, i, t) option remember; (m-> `if`(n>m, 0, `if`(n=m, 1,
%p A290052       add(b(n-j, i-t, 1-t), j=0..min(i, n)))))(i*(i+1-t))
%p A290052     end:
%p A290052 a:= n-> b(n$2, 1):
%p A290052 seq(a(n), n=0..30);
%t A290052 b[n_, i_, t_] := b[n, i, t] = Function[m, If[n > m, 0, If[n == m, 1, Sum[b[n - j, i - t, 1 - t], {j, 0, Min[i, n]}]]]][i*(i + 1 - t)];
%t A290052 a[n_] := b[n, n, 1];
%t A290052 Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Nov 06 2017, after _Alois P. Heinz_ *)
%Y A290052 Main diagonal of A290057.
%Y A290052 Cf. A019589, A014062, A290133.
%K A290052 nonn
%O A290052 0,3
%A A290052 _Alois P. Heinz_, Jul 19 2017