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A290052 Number of X-rays of n X n binary matrices with exactly n ones. 4
1, 1, 4, 23, 139, 860, 5393, 34142, 217717, 1396346, 8997695, 58205686, 377775385, 2458841504, 16043226825, 104901986083, 687221188145, 4509605878736, 29636894936761, 195035340954186, 1285062484293880, 8476508261617168, 55969236979211755, 369900194873712830 (list; graph; refs; listen; history; text; internal format)
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..1000

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

A019589(n) <= a(n) <= A014062(n).

a(n) ~ c * 3^(3*n) / (2^(2*n) * sqrt(n)), where c = 0.153294749730773567280925277269616968259180871352428154276351832424636097919... - Vaclav Kotesovec, Jul 22 2017

EXAMPLE

a(0) = 1: [].

a(1) = 1: 1.

a(2) = 4: 011, 020, 101, 110.

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.

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(n$2, 1):

seq(a(n), n=0..30);

MATHEMATICA

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)];

a[n_] := b[n, n, 1];

Table[a[n], {n, 0, 30}] (* Jean-Fran├žois Alcover, Nov 06 2017, after Alois P. Heinz *)

CROSSREFS

Main diagonal of A290057.

Cf. A019589, A014062, A290133.

Sequence in context: A091640 A237362 A067110 * A158197 A038736 A091642

Adjacent sequences:  A290049 A290050 A290051 * A290053 A290054 A290055

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 19 2017

STATUS

approved

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Last modified March 23 13:17 EDT 2019. Contains 321430 sequences. (Running on oeis4.)