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A188498
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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(j) >= 2 for j=3,4.
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3
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0, 1, 2, 3, 8, 30, 102, 308, 905, 2744, 8473, 26112, 79924, 244204, 747160, 2288521, 7009458, 21461803, 65704200, 201162258, 615922714, 1885853660, 5774072225, 17678809840, 54128358209, 165728860112, 507424764216, 1553620027784, 4756831354752
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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 zeroes in the (1,3) and (1,4)-entries), 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 13 of Klove's Table 3.
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LINKS
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Table of n, a(n) for n=0..28.
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 11 2011 (Start):
a(n) = A188497(n+1) - A188494(n).
a(n) = A002526(n-1) + A002526(n-2).
(End)
G.f.: -(x^10+2*x^9+x^8 -2*x^6-2*x^5-2*x^4 -3*x^3+x) / (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).
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MAPLE
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with(LinearAlgebra):
A188498:= n-> `if` (n=0, 0, Permanent (Matrix (n, (i, j)->
`if` (abs(j-i)<4 and [i, j]<>[1, 3] and [i, j]<>[1, 4] and [i, j]<>[3, 1] and [i, j]<>[4, 1], 1, 0)))):
seq (A188498(n), n=0..20);
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CROSSREFS
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Sequence in context: A186927 A177010 A004106 * A012886 A078918 A054104
Adjacent sequences: A188495 A188496 A188497 * A188499 A188500 A188501
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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 11 2011
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STATUS
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approved
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