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URL: https://oeis.org/A349108

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A349108
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).
3
1, 1, 2, 66, 292, 41100, 314736, 108446352, 1267665984, 829171609920, 13696865136000, 14718069991152000, 325942368613966080, 524455030610743115520, 14983681934750599526400, 33855616071967479729408000, 1211736134642288777186918400, 3668200144503587527675580006400
OFFSET
0,3
COMMENTS
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).
det(A(1)) = 1 and det(A(n)) = 0 for n > 1.
LINKS
FORMULA
a(2*n) = A349107(2*n).
EXAMPLE
For n = 5 the matrix A(5) is
5, 4, 3, 4, 5
4, 3, 2, 3, 4
3, 2, 1, 2, 3
4, 3, 2, 3, 4
5, 4, 3, 4, 5
with permanent a(5) = 41100.
For n = 6 the matrix A(6) is
5, 4, 3, 3, 4, 5
4, 3, 2, 2, 3, 4
3, 2, 1, 1, 2, 3
3, 2, 1, 1, 2, 3
4, 3, 2, 2, 3, 4
5, 4, 3, 3, 4, 5
with permanent a(6) = 314736.
MATHEMATICA
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]]
PROG
(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
CROSSREFS
Cf. A213037 (trace of matrix A(n)), A349107.
Sequence in context: A385100 A075809 A257788 * A226409 A226338 A131472
KEYWORD
nonn
AUTHOR
Stefano Spezia, Nov 08 2021
STATUS
approved