A349107 a(n) is the permanent of the n X n matrix A(n) that is defined as A[i,j,n] = n - abs((n + 1)/2 - i) - abs((n + 1)/2 - j).

1, 1, 2, 22, 292, 9084, 314736, 19224816, 1267665984, 127896194880, 13696865136000, 2061743814864000, 325942368613966080, 68443327006163424000, 14983681934750599526400, 4184458128589740299827200, 1211736134642288777186918400, 434251427188367439407838412800, 160701529762439051943130553548800

Offset: 0

Author

Stefano Spezia, Nov 08 2021

Keywords

• nonn

Comments

A(n) is an n X n matrix whose elements start from 1 at the corners and get higher, the more they are at the center (see the examples).

det(A(1)) = 1 and det(A(n)) = 0 for n > 1.

Examples

			For n = 5 the matrix A(5) is
   1, 2, 3, 2, 1
   2, 3, 4, 3, 2
   3, 4, 5, 4, 3
   2, 3, 4, 3, 2
   1, 2, 3, 2, 1
with permanent a(5) = 9084.
For n = 6 the matrix A(6) is
   1, 2, 3, 3, 2, 1
   2, 3, 4, 4, 3, 2
   3, 4, 5, 5, 4, 3
   3, 4, 5, 5, 4, 3
   2, 3, 4, 4, 3, 2
   1, 2, 3, 3, 2, 1
with permanent a(6) = 314736.
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..36

Crossrefs

Cf. A000982 (trace of matrix A(n)), A317614 (elements sum of matrix A(n)), A349108.

Programs

Mathematica

A[i_, j_, n_] := n - Abs[(n + 1)/2 - i] - Abs[(n + 1)/2 - j]; a[n_]:=Permanent[Table[A[i,j,n],{i,n},{j,n}]]; Array[a,18]

PARI

a(n) = matpermanent(matrix(n, n, i, j, n - abs((n + 1)/2 - i) - abs((n + 1)/2 - j))); \\ Michel Marcus, Nov 08 2021

Formula

a(2*n) = A349108(2*n).