A039917 Number of orderings of 1,2,...,n^2 in an n X n matrix such that each row, each column and both diagonals are increasing.
1, 1, 9, 2017, 21569213, 17835527619513, 1677123511579177202174, 24742950249259362969953039657613, 75512002909758683196631913316950684079768626, 60752021865167494642984305761115275381534124800396484901989, 15991585283632910454908797943467512732011897255095362833558749286619895509557
Offset: 1
Keywords
Examples
From _Alois P. Heinz_, Jul 23 2012: (Start)
a(2) = 1: [1, 3]
[2, 4].
a(3) = 9:
[1, 4, 7] [1, 3, 7] [1, 2, 7] [1, 4, 6] [1, 3, 6]
[2, 5, 8] [2, 5, 8] [3, 5, 8] [2, 5, 8] [2, 5, 8]
[3, 6, 9] [4, 6, 9] [4, 6, 9] [3, 7, 9] [4, 7, 9]
.
[1, 2, 6] [1, 4, 6] [1, 3, 6] [1, 2, 6]
[3, 5, 8] [2, 5, 7] [2, 5, 7] [3, 5, 7]
[4, 7, 9] [3, 8, 9] [4, 8, 9] [4, 8, 9]. (End)
Links
Programs
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Maple
b:= proc(l) option remember; local n; n:= nops(l); `if`({l[]}={0}, 1, add(`if`((l[i]-1<>n-i or i=1 or l[i-1]-1<=n-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..8); # Alois P. Heinz, Jul 23 2012 -
Mathematica
b[l_List] := b[l] = Module[{n = Length[l]}, If[Union[l] == {0}, 1, Sum[If[ (l[[i]]-1 != n-i || i == 1 || l[[i-1]]-1 <= n-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}]]; Array[a, 8] (* Jean-François Alcover, Nov 08 2020, after Alois P. Heinz *)
Extensions
One more term from Jud McCranie, Aug 09 2001
a(6)-a(13) from Alois P. Heinz, Jul 23 2012