A351154 a(n) is the permanent of the n X n matrix M(n) that is defined as M[i,j,n] = A351153(n, min(i, j)) + abs(i - j).

1, 1, 7, 169, 10388, 1324344, 305668180, 116145817656, 67770421715800, 57594670663866124, 68393751368082128320, 109765035421144948709232, 231657098706747226470685920, 628412716450312334529486247152, 2149132484027947970192241804640128, 9113755489596517688997731211571700256

Offset: 0

Author

Stefano Spezia, Feb 02 2022

Keywords

• nonn

Comments

Conjectures: (Start)

det(M(0)) = det(M(1)) = 1 and det(M(n)) = -(n - 2)! for n > 1.

abs(det(M(n))) = abs(A159333(n-2)). (End)

Examples

			a(3) = 169:
    1    2    3
    2    4    5
    3    5    6
a(4) = 10388:
    1    2    3    4
    2    5    6    7
    3    6    8    9
    4    7    9   10
		

Crossrefs

Cf. A000142, A003983, A049581, A159333, A351153.

Programs

Mathematica

A351153[n_,k_]:=n(k-1)-k(k-3)/2; M[i_,j_,n_]:=A351153[n,Min[i,j]]+Abs[i-j]; a[n_]:=Permanent[Table[M[i,j,n],{i,n},{j,n}]]; Join[{1},Array[a,15]]

PARI

t(n, k) = n*(k-1) - k*(k-3)/2; \\ A351153
a(n) = matpermanent(matrix(n, n, i, j, t(n, min(i, j)) + abs(i - j))); \\ Michel Marcus, Feb 03 2022