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0, 0, 2, 4, 12, 32, 108, 336, 1036, 3120, 9540, 29244, 89768, 274788, 840936, 2573972, 7881922, 24135000, 73897320, 226249264, 692714696, 2120941424, 6493883944, 19882820480, 60876609464, 186390208744, 570684661408, 1747307671896, 5349860697088
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 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, p(1) <= 2, and p(2) <= 4.
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 (3,1), (4,1), and (5,2)-entries), and is zero elsewhere.
This is row 9 of Klove's Table 3.
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REFERENCES
| 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
| Nathaniel Johnston, Table of n, a(n) for n = 0..90
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
| a(n) = A002527(n-1) + A188491(n-1). - Nathaniel Johnston, Apr 10 2011
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MAPLE
| with(LinearAlgebra):
A002528:= n-> `if` (n<=1, 0, Permanent (Matrix (n, (i, j)->
`if` (abs(j-i)<4 and [i, j]<>[3, 1] and [i, j]<>[4, 1] and [i, j]<>[5, 2], 1, 0)))):
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CROSSREFS
| Sequence in context: A161177 A039721 A148193 * A148194 A027695 A148195
Adjacent sequences: A002525 A002526 A002527 * A002529 A002530 A002531
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Name and comments edited, and a(12) - a(28) from Nathaniel Johnston (nathaniel(AT)nathanieljohnston.com), Apr 10 2011
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