A351154 - OEIS

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

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OFFSET

0,3

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)

The conjectures are true (see Fried link). - Sela Fried, Feb 13 2026

LINKS

Table of n, a(n) for n=0..15.

Sela Fried, Proof of a conjecture stated in A351154, 2026.

EXAMPLE

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

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]]

PROG

(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

CROSSREFS

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

Sequence in context: A012067 A012145 A368839 * A005019 A172027 A113562

Adjacent sequences: A351151 A351152 A351153 * A351155 A351156 A351157

KEYWORD

nonn

AUTHOR

Stefano Spezia, Feb 02 2022

STATUS

approved