A181191 Number of n X n matrices containing a permutation of 1..n*n in increasing order rowwise, columnwise, diagonally and (downwards) antidiagonally.

1, 1, 4, 169, 141696, 3777546912, 4673805856338368, 368253691037579094795185, 2426023001499238992505630883146240, 1697356437632520242875237327471631991584394752, 156101219875805260212264222801658705937606174957553142873088

Offset: 1

Author

R. H. Hardin, Oct 10 2010

Keywords

• nonn

Examples

			All solutions for 3 X 3:
..1..2..3....1..2..3....1..2..4....1..2..4
..4..5..6....4..5..7....3..5..6....3..5..7
..7..8..9....6..8..9....7..8..9....6..8..9
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20

Crossrefs

Main diagonal of A181196.

Cf. A039917, A181196.

Programs

Maple

b:= proc(l) option remember; local n; n:= nops(l);
      `if`({l[]}={0}, 1, add(`if`((i=1 or l[i-1]<=l[i]) and l[i]>
      `if`(i=n, 0, l[i+1]), b(subsop(i=l[i]-1, l)), 0), i=1..n))
    end:
a:= n-> b([n$n]):
seq(a(n), n=1..10);  # Alois P. Heinz, Jul 24 2012

Mathematica

b[l_] := b[l] = With[{n = Length[l]},
   If[Union[l]=={0}, 1, Sum[If[(i==1 || l[[i-1]] <= l[[i]]) && l[[i]] >
   If[i==n, 0, l[[i+1]]], b[ReplacePart[l, i->l[[i]]-1]], 0], {i, 1, n}]]];
a[n_] := b[Table[n, {n}]];
Table[a[n], {n, 1, 11}] (* Jean-François Alcover, May 10 2022, after Alois P. Heinz *)

Extensions

a(10)-a(16) from Alois P. Heinz, Jul 24 2012