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.
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 19 2017
STATUS
approved