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

0,3

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.

Links

Table of n, a(n) for n=0..14.

Example

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 |

Mathematica

a={1}; For[n=1, n<=14, n++, k=i=j=1; M[i, j]=k++; For[h=1, h<n, h++,  If[i==j==1, M[i, ++j]=k++; For[c=1, c<=h, c++, M[++i, j]=k++; M[i, --j]=k++], If[j==1 && i!=1, M[++i, j]=k++; For[c=1, c<=h, c++, M[i, ++j]=k++]; For[c=1, c<=h, c++, M[--i, j]=k++], If[i==1 &&j!=1, M[i, ++j]=k++; For[c=1, c<=h, c++, M[++i, j]=k++]; For[c=1, c<=h, c++, M[i, --j]=k++]]]]]; AppendTo[a, Permanent[Table[M[i, j], {i, n}, {j, n}]]]]; a

Crossrefs

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

Sequence in context: A049654 A179897 A185203 * A265978 A263184 A370087

Adjacent sequences: A363457 A363458 A363459 * A363461 A363462 A363463

Keyword

nonn

Author

Stefano Spezia, Jun 03 2023

Status

approved