A349108 a(n) is the permanent of the n X n matrix A(n) that is defined as A[i,j,n] = (n mod 2) + abs((n + 1)/2 - i) + abs((n + 1)/2 - j).

1, 1, 2, 66, 292, 41100, 314736, 108446352, 1267665984, 829171609920, 13696865136000, 14718069991152000, 325942368613966080, 524455030610743115520, 14983681934750599526400, 33855616071967479729408000, 1211736134642288777186918400, 3668200144503587527675580006400

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 center and get higher, the more they are close to the corners (see the examples).

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

Examples

			For n = 5 the matrix A(5) is
   5, 4, 3, 4, 5
   4, 3, 2, 3, 4
   3, 2, 1, 2, 3
   4, 3, 2, 3, 4
   5, 4, 3, 4, 5
with permanent a(5) = 41100.
For n = 6 the matrix A(6) is
   5, 4, 3, 3, 4, 5
   4, 3, 2, 2, 3, 4
   3, 2, 1, 1, 2, 3
   3, 2, 1, 1, 2, 3
   4, 3, 2, 2, 3, 4
   5, 4, 3, 3, 4, 5
with permanent a(6) = 314736.
		

Links

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

Crossrefs

Cf. A213037 (trace of matrix A(n)), A349107.

Programs

Mathematica

A[i_, j_, n_] := Mod[n,2]+ Abs[(n + 1)/2 - j] +Abs[(n + 1)/2 - i]; a[n_]:=Permanent[Table[A[i,j,n],{i,n},{j,n}]]; Join[{1},Array[a,17]]

PARI

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

Formula

a(2*n) = A349107(2*n).