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A000804
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Permanent of a certain cyclic n X n (0,1) matrix.
(Formerly M5375 N2333)
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4
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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; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n) is the number of permutations of [ n ] allowing i->i+j (mod n), j=0..4.
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REFERENCES
| 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.
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).
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 0..1000
Index entries for sequences related to binary matrices
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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).
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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);
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CROSSREFS
| Cf. A000805.
Fifth column of triangle A008305. - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 03 2003
Sequence in context: A190393 A083267 A130480 * A048631 A189852 A189564
Adjacent sequences: A000801 A000802 A000803 * A000805 A000806 A000807
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KEYWORD
| nonn,changed
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 03 2003
Edited by Alois P. Heinz (heinz(AT)hs-heilbronn.de), Dec 18 2010
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