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.
FORMULA
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-François Alcover, Nov 06 2017, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 19 2017
STATUS
approved