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A188495
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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(4) >= 2.
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6
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0, 1, 2, 4, 10, 36, 120, 368, 1089, 3304, 10168, 31312, 95880, 293120, 896824, 2746569, 8411818, 25756220, 78853410, 241421436, 739183568, 2263249600, 6929580817, 21216729488, 64960656448, 198894856144, 608971496032, 1864533223584, 5708777321872
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OFFSET
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0,3
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COMMENTS
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a(n) is also the permanent of the n-by-n matrix that has ones on its diagonal, ones on its three superdiagonals (with the exception of a zero in the (1,4)-entry), ones on its three subdiagonals (with the exception of zeroes in the (3,1) and (4,1)-entries), and is zero elsewhere.
This is row 10 of Klove's Table 3.
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LINKS
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Nathaniel Johnston, Table of n, a(n) for n = 0..119
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.
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FORMULA
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Contribution from Nathaniel Johnston, Apr 10 2011 (Start):
a(n) = A188493(n+1) - A188491(n) - A188497(n).
a(n) = A002526(n-1) + A188494(n-1).
(End)
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MAPLE
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with (LinearAlgebra):
A188495:= n-> `if` (n=0, 0, Permanent (Matrix (n, (i, j)->
`if` (abs(j-i)<4 and [i, j]<>[3, 1] and [i, j]<>[4, 1] and [i, j]<>[1, 4], 1, 0)))):
seq (A188495(n), n=0..20);
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CROSSREFS
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Sequence in context: A125859 A103854 A126941 * A038077 A006396 A192502
Adjacent sequences: A188492 A188493 A188494 * A188496 A188497 A188498
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Apr 01 2011
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EXTENSIONS
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Name and comments edited, and a(12) - a(28) from Nathaniel Johnston, Apr 10 2011
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STATUS
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approved
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