A349108 - OEIS

%I #9 Nov 09 2021 04:42:26

%S 1,1,2,66,292,41100,314736,108446352,1267665984,829171609920,

%T 13696865136000,14718069991152000,325942368613966080,

%U 524455030610743115520,14983681934750599526400,33855616071967479729408000,1211736134642288777186918400,3668200144503587527675580006400

%N a(n) is the permanent of the n X n matrix A(n) that is defined as A[i,j,n] = (n mod 2) + 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 center and get higher, the more they are close to the corners (see the examples).

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

%H Vaclav Kotesovec, <a href="/A349108/b349108.txt">Table of n, a(n) for n = 0..36</a>

%F a(2*n) = A349107(2*n).

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

%e    5, 4, 3, 4, 5

%e    4, 3, 2, 3, 4

%e    3, 2, 1, 2, 3

%e    4, 3, 2, 3, 4

%e    5, 4, 3, 4, 5

%e with permanent a(5) = 41100.

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

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

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

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

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

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

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

%e with permanent a(6) = 314736.

%t A[i_, j_, n_] := Mod[n,2]+ Abs[(n + 1)/2 - j] +Abs[(n + 1)/2 - i]; a[n_]:=Permanent[Table[A[i,j,n],{i,n},{j,n}]]; Join[{1},Array[a,17]]

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

%Y Cf. A213037 (trace of matrix A(n)), A349107.

%K nonn

%O 0,3

%A _Stefano Spezia_, Nov 08 2021