A330287 Permanent of the n-th principal submatrix M(n) of A319840.

1, 1, 8, 208, 11488, 1093056, 158972160, 32734095360, 9049229328384, 3230305304002560, 1445344680438005760, 791762592707031859200, 521023492500173338705920, 405448567547957922512240640, 368210800911998093644372377600, 385879616532879866123928993792000, 462151848929747968377341029122048000

Offset

0,3

Comments

The matrix M(n) is defined as M[i,j,n] = i*j if i < 3 or j < 3 and M[i,j,n] = 2*(i + j) - 4 otherwise.

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

For n > 0, the trace of the matrix M(n) is A001844(n-1).

For n > 0, the antitrace of the matrix M(n) is A005893(n-1).

For n > 1, the super- and subdiagonal sum is A001105(n-1).

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..35

Formula

a(n) ~ c * A238261^n * n!^2 / sqrt(n), where c = 0.0286685259829... - Vaclav Kotesovec, Aug 19 2021

Example

For n = 1 the matrix M(1) is
  1
with permanent a(1) = 1.
For n = 2 the matrix M(2) is
  1, 2
  2, 4
with permanent a(2) = 8.
For n = 3 the matrix M(3) is
  1,  2,  3
  2,  4,  6
  3,  6,  8
with permanent a(3) = 208.

Prog

(PARI) tm(n) = matrix(n, n, i, j, if ((i<3) || (j<3), i*j, 2*(i+j)-4));
a(n) = matpermanent(tm(n));

Crossrefs

Cf. A001105, A001844, A005893, A319840.

Sequence in context: A090962 A359281 A359452 * A279663 A294970 A275286

Adjacent sequences: A330284 A330285 A330286 * A330288 A330289 A330290

Keyword

nonn

Author

Stefano Spezia, Dec 11 2019

Status

approved