login
A340900
a(n) is the number of permutations pi on n letters such that pi(i) != i (mod 3) for all i.
1
1, 0, 1, 2, 4, 16, 80, 288, 1728, 12096, 67392, 525312, 4783104, 35942400, 349056000, 3891456000, 36910080000, 429981696000, 5667397632000, 64963067904000, 883878137856000, 13437405757440000, 180681897811968000, 2813727217287168000, 48450827875516416000
OFFSET
0,4
COMMENTS
a(n) is the permanent of the n X n matrix given by f(i,j) = ((i-j)^2 mod 3).
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..35 (terms 0..33 from Pontus von Brömssen)
FORMULA
a(3*n) = A204436(3*n) = A204438(3*n) = A204440(3*n),
a(3*n+1) = A204438(3*n+1), and
a(3*n+2) = A204436(3*n+2).
EXAMPLE
For n = 4, the a(4) = 4 allowable permutations (read as words) are
(2,4,1,3),
(2,1,4,3),
(3,4,1,2), and
(3,1,4,2).
These are all of the permutations in S_4 subject to the restriction that the first letter cannot be 1 or 4, the second letter cannot be 2, the third letter cannot be 3, and the fourth letter cannot be 1 or 4.
MATHEMATICA
contingency[n_] := Table[Mod[(i - j)^2, 3], {i, 1, n}, {j, 1, n}];
a[0] := 1;
a[n_] := Permanent[contingency[n]];
PROG
(PARI) a(n) = matpermanent(matrix(n, n, i, j, (i-j)^2 % 3)); \\ Michel Marcus, Jan 27 2021
CROSSREFS
Analogous sequences: A204436 (pi(i) + i != 0), A204438 (pi(i) + i != 2), A204440 (pi(i) + i != 1).
Sequence in context: A275555 A370485 A058926 * A347631 A102736 A247007
KEYWORD
nonn
AUTHOR
Peter Kagey, Jan 25 2021
EXTENSIONS
a(23)-a(24) from Alois P. Heinz, Jan 27 2021
STATUS
approved