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A349107
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).
3
1, 1, 2, 22, 292, 9084, 314736, 19224816, 1267665984, 127896194880, 13696865136000, 2061743814864000, 325942368613966080, 68443327006163424000, 14983681934750599526400, 4184458128589740299827200, 1211736134642288777186918400, 434251427188367439407838412800, 160701529762439051943130553548800
OFFSET
0,3
COMMENTS
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).
det(A(1)) = 1 and det(A(n)) = 0 for n > 1.
LINKS
FORMULA
a(2*n) = A349108(2*n).
EXAMPLE
For n = 5 the matrix A(5) is
1, 2, 3, 2, 1
2, 3, 4, 3, 2
3, 4, 5, 4, 3
2, 3, 4, 3, 2
1, 2, 3, 2, 1
with permanent a(5) = 9084.
For n = 6 the matrix A(6) is
1, 2, 3, 3, 2, 1
2, 3, 4, 4, 3, 2
3, 4, 5, 5, 4, 3
3, 4, 5, 5, 4, 3
2, 3, 4, 4, 3, 2
1, 2, 3, 3, 2, 1
with permanent a(6) = 314736.
MATHEMATICA
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]
PROG
(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
CROSSREFS
Cf. A000982 (trace of matrix A(n)), A317614 (elements sum of matrix A(n)), A349108.
Sequence in context: A156505 A367979 A256928 * A368447 A299824 A355724
KEYWORD
nonn
AUTHOR
Stefano Spezia, Nov 08 2021
STATUS
approved