A349099 a(n) is the permanent of the n X n matrix M(n) defined as M(n)[i,j] = i*j (mod n + 1).

1, 1, 5, 32, 1074, 12600, 1525292, 34078720, 4072850100, 263459065600, 106809546673488, 2254519427530752, 3172225081523720416, 210351382651302645760, 45654014718074873700000, 11122845097194072534155264, 18156837198112938091803999360, 795289872611524024920215715840

Offset

0,3

Comments

Det(M(n)) = 0 iff n = 4 or n > 5.

Rank(M(n)) = A088922(n+1).

Tr(M(n)) = A048153(n+1).

Links

Table of n, a(n) for n=0..17.

Example

See A352620 for the examples of matrix M(n).

Maple

a:= n-> `if`(n=0, 1, LinearAlgebra[Permanent](
         Matrix(n, (i, j)-> (i*j) mod (n+1)))):
seq(a(n), n=0..16);  # Alois P. Heinz, Mar 25 2022

Mathematica

Join[{1}, Table[Permanent[Table[Mod[j*Table[i, {i, n}], n+1], {j, n}]], {n, 17}]]

Prog

(PARI) a(n) = matpermanent(matrix(n, n, i, j, (i*j)%(n+1))); \\ Michel Marcus, Mar 26 2022

Crossrefs

Cf. A352620.

Cf. A048153, A074930, A088922, A160255.

Sequence in context: A125709 A363314 A203112 * A174471 A275233 A359971

Adjacent sequences: A349096 A349097 A349098 * A349100 A349101 A349102

Keyword

nonn

Author

Stefano Spezia, Mar 25 2022

Status

approved