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URL: https://oeis.org/A000804

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A000804
Permanent of a certain cyclic n X n (0,1) matrix.
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
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
N. Metropolis et al., Permanents of cyclic (0,1) matrices, J. Combin. Theory, 7 (1969), 291-321.
H. Minc, Permanents of (0,1)-circulants, Canad. Math. Bull., 7 (1964), 253-263.
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
Cf. A000805.
Fifth column of triangle A008305. - Vladeta Jovovic, Oct 03 2003
Cf. A260074. - Alois P. Heinz, Jul 14 2015
Sequence in context: A263699 A083267 A130480 * A048631 A263700 A263701
KEYWORD
nonn
EXTENSIONS
More terms from Vladeta Jovovic, Oct 03 2003
Edited by Alois P. Heinz, Dec 18 2010
STATUS
approved