A349107 - OEIS

%I #10 Nov 09 2021 04:41:42

%S 1,1,2,22,292,9084,314736,19224816,1267665984,127896194880,

%T 13696865136000,2061743814864000,325942368613966080,

%U 68443327006163424000,14983681934750599526400,4184458128589740299827200,1211736134642288777186918400,434251427188367439407838412800,160701529762439051943130553548800

%N a(n) is the permanent of the n X n matrix A(n) that is defined as A[i,j,n] = n - abs((n + 1)/2 - i) - abs((n + 1)/2 - j).

%C A(n) is an n X n matrix whose elements start from 1 at the corners and get higher, the more they are at the center (see the examples).

%C det(A(1)) = 1 and det(A(n)) = 0 for n > 1.

%H Vaclav Kotesovec, <a href="/A349107/b349107.txt">Table of n, a(n) for n = 0..36</a>

%F a(2*n) = A349108(2*n).

%e For n = 5 the matrix A(5) is

%e    1, 2, 3, 2, 1

%e    2, 3, 4, 3, 2

%e    3, 4, 5, 4, 3

%e    2, 3, 4, 3, 2

%e    1, 2, 3, 2, 1

%e with permanent a(5) = 9084.

%e For n = 6 the matrix A(6) is

%e    1, 2, 3, 3, 2, 1

%e    2, 3, 4, 4, 3, 2

%e    3, 4, 5, 5, 4, 3

%e    3, 4, 5, 5, 4, 3

%e    2, 3, 4, 4, 3, 2

%e    1, 2, 3, 3, 2, 1

%e with permanent a(6) = 314736.

%t A[i_, j_, n_] := n - Abs[(n + 1)/2 - i] - Abs[(n + 1)/2 - j]; a[n_]:=Permanent[Table[A[i,j,n],{i,n},{j,n}]]; Array[a,18]

%o (PARI) a(n) = matpermanent(matrix(n, n, i, j, n - abs((n + 1)/2 - i) - abs((n + 1)/2 - j))); \\ _Michel Marcus_, Nov 08 2021

%Y Cf. A000982 (trace of matrix A(n)), A317614 (elements sum of matrix A(n)), A349108.

%K nonn

%O 0,3

%A _Stefano Spezia_, Nov 08 2021