A290058 Number of X-rays of n X n binary matrices with exactly floor(n^2/2) ones.

1, 1, 4, 30, 440, 9892, 331950, 15121926, 915201732, 70120569074, 6696969703276, 774618119733020, 107284227278413622, 17455779156567652806, 3307802489634916900474, 720231707823173636419042, 178973636259170839478327332, 50249140887232774758578932120

Offset

0,3

Comments

The X-ray of a matrix is defined as the sequence of antidiagonal sums.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..253

C. Bebeacua, T. Mansour, A. Postnikov and S. Severini, On the X-rays of permutations, arXiv:math/0506334 [math.CO], 2005.

Index entries for sequences related to binary matrices

Formula

a(n) = A290057(n,floor(n^2/2)).

a(n) ~ 6*sqrt(Pi) * n^(2*n+1/2) / exp(2*n). - Vaclav Kotesovec, Jul 22 2017

Example

a(2) = 4: 011, 020, 101, 110.
a(3) = 30: 00121, 00211, 00220, 00301, 00310, 01021, 01111, 01120, 01201, 01210, 01300, 02011, 02020, 02101, 02110, 02200, 10021, 10111, 10120, 10201, 10210, 10300, 11011, 11020, 11101, 11110, 11200, 12001, 12010, 12100.

Maple

b:= proc(n, i, t) option remember; (m-> `if`(n>m, 0, `if`(n=m, 1,
      add(b(n-j, i-t, 1-t), j=0..min(i, n)))))(i*(i+1-t))
    end:
a:= n-> b(iquo(n^2, 2), n, 1):
seq(a(n), n=0..20);

Mathematica

b[n_, i_, t_]:= b[n, i, t] = Function[{m, jm}, If[n>m, 0, If[n==m, 1, Sum[b[n-j, i-t, 1-t], {j, 0, jm}]]]][i*(i+1-t), Min[i, n]]; a[n_]:=  b[Quotient[n^2, 2], n, 1]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Aug 09 2017, translated from Maple *)

Crossrefs

Cf. A290057, A290134.

Sequence in context: A363911 A326205 A351795 * A168129 A193500 A163885

Adjacent sequences: A290055 A290056 A290057 * A290059 A290060 A290061

Keyword

nonn

Author

Alois P. Heinz, Jul 19 2017

Status

approved