A363460 a(n) is the permanent of the n X n matrix formed by placing 1..n^2 in L-shaped gnomons in alternating directions.

1, 1, 11, 556, 74964, 21700112, 11500685084, 10057140949968, 13496937368200000, 26331147893897760544, 71606290155732170272320, 262516365211410942628577408, 1262517559940020030446967822592, 7786463232979127181938238723356160, 60414239829783205320232261233394491136

Offset: 0

Author

Stefano Spezia, Jun 03 2023

Keywords

• nonn

Comments

The matrix is the upper-left n X n part of the square arrangement in A081344.

The matrix element k is at row A220604(k) and column A220603(k), for k = 1..n^2.

Examples

			a(5) = 21700112 is the permanent of the 5 X 5 matrix
  |  1----2    9---10   25 |
  |       |    |    |    | |
  |  4----3    8   11   24 |
  |  |         |    |    | |
  |  5----6----7   12   23 |
  |                 |    | |
  | 16---15---14---13   22 |
  |  |                   | |
  | 17---18---19---20---21 |
		

Crossrefs

Cf. A006527 (trace), A037270 (elements sum of the matrix), A060736, A061349 (anti trace), A081344, A220603, A220604, A363376 (determinant).

Programs

Mathematica

a={1}; For[n=1, n<=14, n++,k=i=j=1; M[i,j]=k++; For[h=1, h