

A188498


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.


3



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

0,3


COMMENTS

a(n) is also the permanent of the nbyn 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.


LINKS

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.


FORMULA

Contribution from Nathaniel Johnston, Apr 11 2011 (Start):
a(n) = A188497(n+1)  A188494(n).
a(n) = A002526(n1) + A002526(n2).
(End)
G.f.: (x^10+2*x^9+x^8 2*x^62*x^52*x^4 3*x^3+x) / (x^14+2*x^13+2*x^11 +4*x^102*x^910*x^8 16*x^72*x^6+8*x^5 +10*x^4+2*x^2+2*x1).


MAPLE

with(LinearAlgebra):
A188498:= n> `if` (n=0, 0, Permanent (Matrix (n, (i, j)>
`if` (abs(ji)<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);


CROSSREFS

Sequence in context: A186927 A177010 A004106 * A012886 A078918 A054104
Adjacent sequences: A188495 A188496 A188497 * A188499 A188500 A188501


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Apr 01 2011


EXTENSIONS

Name and comments edited, and a(12)  a(28) from Nathaniel Johnston, Apr 11 2011


STATUS

approved



