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0, 0, 2, 6, 18, 46, 146, 460, 1436, 4352, 13252, 40532, 124396, 381140, 1166708, 3570684, 10932274, 33475170, 102499334, 313825690, 960844358, 2941873064, 9007393480, 27578681888, 84439657768, 258534813320, 791574775192, 2423623112104, 7420586212184, 22720153701768, 69563959091138
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OFFSET
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0,3
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COMMENTS
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For n >= 2, a(n) is the number of permutations p on the set [n] with the properties that abs(p(i)-i) <= 3 for all i and p(j) <= 2+j for j = 1,2.
For n >= 2, a(n) is also the permanent of the n-by-n matrix that has ones on its diagonal, ones on its three superdiagonals, ones on its three subdiagonals (with the exception of zeroes in the (4,1) and (5,2)-entries), and is zero elsewhere.
This is row 3 of Klove's Table 3.
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REFERENCES
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R. Lagrange, Quelques re'sultats dans la me'trique des permutations, Annales Scientifiques de l'\'{E}cole Normale Sup\'{e}rieure, Paris, 79 (1962), 199-241.
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
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Table of n, a(n) for n=0..30.
Torleiv Klove, Spheres of Permutations under the Infinity Norm - Permutations with limited displacement. Reports in Informatics, Department of Informatics, University of Bergen, Norway, no. 376, November 2008.
R. Lagrange, Quelques re'sultats dans la me'trique des permutations, Annales Scientifiques de l'\'{E}cole Normale Sup\'{e}rieure, Paris, 79 (1962), 199-241.
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FORMULA
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a(n) = A188379(n+1) - A188492(n) - A188493(n). - Nathaniel Johnston, Apr 08 2011
G.f.: 2*x^2 * (x^4+x^3-x^2-x-1) / (x^14+2*x^13+2*x^11 +4*x^10-2*x^9-10*x^8 -16*x^7-2*x^6 +8*x^5+10*x^4 +2*x^2+2*x-1). - Alois P. Heinz, Apr 08 2011
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MAPLE
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with (LinearAlgebra):
A002529:= n-> `if` (n<=1, 0, Permanent (Matrix (n, (i, j)->
`if` (abs(j-i)<4 and [i, j]<>[4, 1] and [i, j]<>[5, 2], 1, 0)))):
seq (A002529(n), n=0..20);
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CROSSREFS
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Sequence in context: A054136 A140960 A072827 * A217526 A018027 A218759
Adjacent sequences: A002526 A002527 A002528 * A002530 A002531 A002532
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Name and comments edited and terms a(12) - a(30) from Nathaniel Johnston, Apr 08 2011
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STATUS
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approved
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