|
|
A000804
|
|
Permanent of a certain cyclic n X n (0,1) matrix.
(Formerly M5375 N2333)
|
|
5
|
|
|
1, 1, 2, 6, 24, 120, 265, 579, 1265, 2783, 6208, 13909, 31337, 70985, 161545, 369024, 845825, 1944295, 4480285, 10345391, 23930320, 55435605, 128577253, 298529333, 693718721, 1613210120, 3753680073, 8738534315, 20351593033, 47413960239, 110493496000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
a(n) is the number of permutations of [ n ] allowing i->i+j (mod n), j=0..4.
|
|
REFERENCES
|
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
LINKS
|
Index entries for linear recurrences with constant coefficients, signature (3, 0, -2, -2, -6, 2, 4, 2, 2, -1, -1).
|
|
FORMULA
|
G.f.: (41*x^15 +64*x^14 -48*x^13 -113*x^12 -213*x^11 -190*x^10 +122*x^9 +158*x^8 +150*x^7 +75*x^6 -60*x^5 -10*x^4 -2*x^3 +x^2 +2*x -1) / (-x^11 -x^10 +2*x^9 +2*x^8 +4*x^7 +2*x^6 -6*x^5 -2*x^4 -2*x^3 +3*x -1).
|
|
MAPLE
|
a:= n-> `if`(n<5, n!, (Matrix(11, (i, j)-> if i+1=j then 1 elif i=11 then [-1, -1, 2, 2, 4, 2, -6, -2, -2, 0, 3][j] else 0 fi)^(n+6). <<41, -16, 33, -1, 5, -1, 16, 5, 13, 29, 65>>)[1, 1]): seq(a(n), n=0..30);
|
|
MATHEMATICA
|
a[n_] := If[n<5, n!, ((Table[Which[i+1 == j, 1, i == 11, {-1, -1, 2, 2, 4, 2, -6, -2, -2, 0, 3}[[j]], True, 0], {i, 1, 11}, {j, 1, 11}] // MatrixPower[#, n+6]&).{41, -16, 33, -1, 5, -1, 16, 5, 13, 29, 65}) // First]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Mar 17 2014, after Alois P. Heinz *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|